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SOLITON SOLUTIONS FOR THE TWO-DIMENSIONAL LOCAL FRACTIONAL BOUSSINESQ EQUATION Fractals (IF 4.7) Pub Date : 2024-05-09 KUN YIN, XINGJIE YAN
In this work we study the two-dimensional local fractional Boussinesq equation. Based on the basic definitions and properties of the local fractional derivatives and bilinear form, we studied the soliton solutions of non-differentiable type with the generalized functions defined on Cantor sets by using bilinear method. Meanwhile, we discuss the result when fractal dimension is 1, and compare it with
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FRACTAL CHARACTERISTICS OF CORE DISKING FRACTURE SURFACES Fractals (IF 4.7) Pub Date : 2024-05-09 JIA-SHUN LUO, YA-CHEN XIE, JIAN-XING LIAO, XU-NING WU, YAN-LI FANG, LIANG-CHAO HUANG, MING-ZHONG GAO, MICHAEL Z. HOU
The morphological characteristics of core disking can reflect the in-situ stress field characteristics to a certain extent, but a quantitative description method for disking-induced fracture surfaces is needed. The fractal geometry was introduced to refine the three-dimensional characteristics of the core disking fracture surfaces, and the disking mechanism was explored through morphological characteristics
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AN IMAGE ENCRYPTION TECHNIQUE BASED ON DISCRETE WAVELET TRANSFORM AND FRACTIONAL CHAOTIC CRYPTOVIROLOGY Fractals (IF 4.7) Pub Date : 2024-05-08 WALAA M. ABD-ELHAFIEZ, MAHMOUD ABDEL-ATY, XIAO-JUN YANG, AWATEF BALOBAID
In this paper, we present a new encryption method based on discrete wavelet transform (DWT). This method provides a number of advantages as a pseudo randomness and sensitivity due to the variation of the initial values. We start by decomposing the image with spatial reconstruction by DWT, followed by preformation by fractional chaotic cryptovirology and Henon map keys for space encryption. Bearing
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NEW CONJECTURES FOR THE ENTIRE FUNCTIONS ASSOCIATED WITH FRACTIONAL CALCULUS Fractals (IF 4.7) Pub Date : 2024-05-08 XIAO-JUN YANG
In this paper, we address the entire Fourier sine and cosine integrals related to the Mittag-Leffler function. We guess that the entire functions have the real zeros in the entire complex plane. They can be connected with the well-known conjectures in analytic number theory. They are considered as the special solutions for the time-fractional diffusion equation within the Caputo fractional derivative
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ON A TEMPERED XI FUNCTION ASSOCIATED WITH THE RIEMANN XI FUNCTION Fractals (IF 4.7) Pub Date : 2024-05-07 XIAO-JUN YANG
In this paper, we propose a tempered xi function obtained by the recombination of the decomposable functions for the Riemann xi function for the first time. We first obtain its functional equation and series representation. We then suggest three equivalent open problems for the zeros for it. We finally consider its behaviors on the critical line.
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THE SCALING-LAW FLOWS: AN ATTEMPT AT SCALING-LAW VECTOR CALCULUS Fractals (IF 4.7) Pub Date : 2024-05-07 XIAO-JUN YANG
In this paper, the scaling-law vector calculus, which is connected between the vector calculus and the scaling law in fractal geometry, is addressed based on the Leibniz derivative and Stieltjes integral for the first time. The scaling-law Gauss–Ostrogradsky-like, Stokes-like and Green-like theorems, and Green-like identities are considered in sense of the scaling-law vector calculus. The strong and
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NEW SPECIAL FUNCTIONS APPLIED TO REPRESENT THE WEIERSTRASS–MANDELBROT FUNCTION Fractals (IF 4.7) Pub Date : 2024-05-04 XIAO-JUN YANG, LU-LU GENG, YU-RONG FAN
This work is devoted to the subtrigonometric and subhyperbolic functions in terms of theWiman class for the first time. The conjectures for the subsine and subcosine functions are considered in detail. The Weierstrass–Mandelbrot function is represented as the hyperbolic subsine, and hyperbolic subcosine functions to get new results for the nondifferentiable functions.
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EXACT TRAVELING WAVE SOLUTIONS OF THE COUPLED LOCAL FRACTIONAL NONLINEAR SCHRÖDINGER EQUATIONS FOR OPTICAL SOLITONS ON CANTOR SETS Fractals (IF 4.7) Pub Date : 2024-05-04 LEI FU, YUAN-HONG BI, JING-JING LI, HONG-WEI YANG
Optical soliton is a physical phenomenon in which the waveforms and energy of optical fibers remain unchanged during propagation, which has important application value in information transmission. In this paper, the coupled nonlinear Schrödinger equations describe the propagation of optical solitons with different frequencies in sense of local fractional derivative is analyzed. The exact traveling
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ANOMALOUS DIFFUSION MODELS AND MANDELBROT SCALING-LAW SOLUTIONS Fractals (IF 4.7) Pub Date : 2024-05-04 XIAO-JUN YANG, ABDULRAHMAN ALI ALSOLAMI, XIAO-JIN YU
In this paper, the anomalous diffusion models are studied in the framework of the scaling-law calculus with the Mandelbrot scaling law. A analytical technology analogous to the Fourier transform is proposed to deal with the one-dimensional scaling-law diffusion equation. The scaling-law series formula via Kohlrausch–Williams–Watts function is efficient and accurate for finding exact solutions for the
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CALCULUS OPERATORS AND SPECIAL FUNCTIONS ASSOCIATED WITH KOHLRAUSCH–WILLIAMS–WATTS AND MITTAG-LEFFLER FUNCTIONS Fractals (IF 4.7) Pub Date : 2024-05-04 XIAO-JUN YANG, LU-LU GENG, YU-MEI PAN, XIAO-JIN YU
In this paper, many important formulas of the subtrigonometric, subhyperbolic, pretrigonometric, prehyperbolic, supertrigonometric, and superhyperbolic functions sin Wiman class are developed for the first time. The subsine, subcosine, subhyperbolic sine, and subhyperbolic cosine associated with Kohlrausch–Williams–Watts (KWW) function and their scaling-law ODEs are proposed. The supersine, supercosine
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LOCAL FRACTIONAL VARIATIONAL ITERATION TRANSFORM METHOD: A TOOL FOR SOLVING LOCAL FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS Fractals (IF 4.7) Pub Date : 2024-05-03 HOSSEIN JAFARI, HASSAN KAMIL JASSIM, ALI ANSARI, VAN THINH NGUYEN
In this paper, we use the local fractional variational iteration transform method LFVITM to solve a class of linear and nonlinear partial differential equations (PDEs), as well as a system of PDEs which are involving local fractional differential operators (LFDOs). The technique combines the variational iteration transform approach and the Yang–Laplace transform. To show how effective and precise the
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LAPLACE DECOMPOSITION METHOD FOR SOLVING THE TWO-DIMENSIONAL DIFFUSION PROBLEM IN FRACTAL HEAT TRANSFER Fractals (IF 4.7) Pub Date : 2024-05-03 HOSSEIN JAFARI, HASSAN KAMIL JASSIM, CANAN ÜNLÜ, VAN THINH NGUYEN
In this paper, the Local Fractional Laplace Decomposition Method (LFLDM) is used for solving a type of Two-Dimensional Fractional Diffusion Equation (TDFDE). In this method, first we apply the Laplace transform and its inverse to the main equation, and then the Adomian decomposition is used to obtain approximate/analytical solution. The accuracy and applicability of the LFLDM is shown through two examples
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A SHORT SOLUTION OF THE LOCAL FRACTIONAL (2+1)-DIMENSIONAL DISPERSIVE LONG WATER WAVE SYSTEM Fractals (IF 4.7) Pub Date : 2024-04-30 FATMA BERNA BENLI, HACI MEHMET BASKONUS, WEI GAO
In this paper, a local fractional Riccati differential equation method is applied. A new travelling wave solution to the nonlinear local fractional (2+1)-dimensional dispersive long water wave system is investigated. After travelling wave transformation, the governing model studied is converted into nonlinear ordinary differential equation. Some properties with the strain conditions are also reported
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A NEW FRACTIONAL DERIVATIVE MODEL FOR THE NON-DARCIAN SEEPAGE Fractals (IF 4.7) Pub Date : 2024-04-30 PEITAO QIU, LIANYING ZHANG, CHAO MA, BING LI, JIONG ZHU, YAN LI, YANG YU, XIAOXI BI
In this paper, a new fractional derivative model for the non-Darcian seepage within the exponential decay kernel is addressed for the first time. The new fractional derivative model is for high-speed non-Darcian and low-speed non-Darcian seepage, in which the applied zone is enlarged.
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APPROXIMATE SOLUTION FOR TIME FRACTIONAL NONLINEAR MKDV EQUATION WITHIN LOCAL FRACTIONAL OPERATORS Fractals (IF 4.7) Pub Date : 2024-04-30 JIAN-SHE SUN
In this paper, we first propose a method, which is originated from coupling local fractional Yang–Laplace transform with the Daftardar–Gejji–Jafaris method (LFYLTDGJM). The proposed method is successfully applied to solve the local time fractional nonlinear modified Korteweg–de Vries (TFNMKDV) equation. The approximate solution presented here illustrates the efficiency and accuracy of the proposed
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A NEW FREQUENCY AMPLITUDE FORMULA FOR THE LOCAL FRACTIONAL NONLINEAR OSCILLATION VIA LOCAL FRACTIONAL CALCULUS Fractals (IF 4.7) Pub Date : 2024-04-30 YONG-JU YANG, MING-CHAI YU, XUE-QIANG WANG
In this paper, we propose a new frequency amplitude formula for the local fractional nonlinear oscillation via local fractional calculus. It is more general than the He’s frequency amplitude formula. Several test cases of local fractional nonlinear oscillations are given to prove the feasibility of the improved formula.
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ON GENERAL LOCAL FRACTIONAL INTEGRAL INEQUALITIES FOR GENERALIZED H-PREINVEX FUNCTIONS ON YANG’S FRACTAL SETS Fractals (IF 4.7) Pub Date : 2024-04-30 YONG ZHANG, WENBING SUN
In this paper, based on Yang’s fractal theory, the Hermite–Hadamard’s inequalities for generalized h-preinvex function are proved. Then, using the local fractional integral identity proposed by Sun [Some local fractional integral inequalities for generalized preinvex functions and applications to numerical quadrature, Fractals27(5) (2019) 1950071] as auxiliary function, some parameterized local fractional
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A NEW FRACTAL MODELING FOR THE NERVE IMPULSES BASED ON LOCAL FRACTIONAL DERIVATIVE Fractals (IF 4.7) Pub Date : 2024-04-30 CHUN-FU WEI
In this paper, a new fractal nerve impulses modeling is successfully described via the Yang’s local fractional derivative in a microgravity space, and its approximate analytical solution is obtained by a new Adomian decomposition method. The efficiency and accuracy analysis of the proposed method is elucidated according to the graphs. The result shows that our method is excellent and accurate in dealing
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A HILBERT-TYPE LOCAL FRACTIONAL INTEGRAL INEQUALITY WITH THE KERNEL OF A HYPERBOLIC COSECANT FUNCTION Fractals (IF 4.7) Pub Date : 2024-04-30 YINGDI LIU, QIONG LIU
By using Yang’s local fractional calculus theory, the method of weight function, and real-analysis techniques in the fractal set, a general Hilbert-type local fractional integral inequality with the kernel of a hyperbolic cosecant function is established. The necessary and sufficient condition for the constant factor of the general Hilbert-type local fractional integral inequality to be the best possible
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EUROPEAN OPTION PRICING IN THE GENERALIZED MIXED WEIGHTED FRACTIONAL BROWNIAN MOTION Fractals (IF 4.7) Pub Date : 2024-04-30 FENG XU, MIAO HAN
In order to describe the self-similarity and long-range dependence of financial asset prices, this paper adopts a new fractional-type process, i.e, the generalized mixed weighted fractional Brownian motion to describe the dynamic change process of risky asset prices. A European option pricing model driven by the generalized mixed weighted fractional Brownian motion is constructed, and explicit solutions
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LYAPUNOV-TYPE INEQUALITY FOR CERTAIN HALF-LINEAR LOCAL FRACTIONAL ORDINARY DIFFERENTIAL EQUATIONS Fractals (IF 4.7) Pub Date : 2024-04-26 HAIDONG LIU, JINGJING WANG
In this paper, we establish a Lyapunov-type inequality for the half-linear local fractional ordinary differential equation based on the formulation of the local fractional derivative. In addition, we apply the inequality to investigate the non-existence and uniqueness of solutions for related homogeneous and non-homogeneous local fractional boundary value problems.
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DISTRIBUTIONAL INVARIANCE IN BINARY MULTIPLICATIVE CASCADES Fractals (IF 4.7) Pub Date : 2024-04-30 CÉSAR AGUILAR-FLORES, ALIN-ANDREI CARSTEANU
The stability properties of certain probability distribution functions under the combined effects of cascading and “dressing” in a binary multiplicative cascade are contemplated and proven herein. Their main importance for applications resides in parameterizing the multiplicative cascade generators of multifractal measures from single realizations, given the generic lack of distributional ergodicity
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ANISOTROPY AND SIZE EFFECT OF THE FRACTAL CHARACTERISTICS OF ROCK FRACTURE SURFACES UNDER MICROWAVE IRRADIATION: AN EXPERIMENTAL RESEARCH Fractals (IF 4.7) Pub Date : 2024-04-25 BEN-GAO YANG, JING XIE, YI-MING YANG, JUN-JUN LIU, SI-QI YE, RUI-FENG TANG, MING-ZHONG GAO
Studying the rough structure characteristics of rock fracture surfaces under microwave irradiation is of a great significance for understanding the rock-breaking mechanism. Therefore, this work takes fracture surface as the research object under three failure modes: microwave irradiation, uniaxial loading and microwave-uniaxial loading. The undulation and roughness are used to describe the morphological
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THE FRACTAL STRUCTURE OF ANALYTICAL SOLUTIONS TO FRACTIONAL RICCATI EQUATION Fractals (IF 4.7) Pub Date : 2024-04-25 ZENONAS NAVICKAS, TADAS TELKSNYS, INGA TELKSNIENE, ROMAS MARCINKEVICIUS, MINVYDAS RAGULSKIS
Analytical solutions to the fractional Riccati equation are considered in this paper. Solutions to fractional differential equations are expressed in the form of fractional power series in the Caputo algebra. It is demonstrated that solutions to higher-order Riccati fractional equations inherit some solutions from lower-order Riccati equations under special initial conditions. Such nested and fractal-like
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VARIATIONAL PERSPECTIVE TO (2+1)-DIMENSIONAL KADOMTSEV–PETVIASHVILI MODEL AND ITS FRACTAL MODEL Fractals (IF 4.7) Pub Date : 2024-04-25 KANG-LE WANG
In this work, the (2+1)-dimensional Kadomtsev–Petviashvili model is investigated. A novel variational scheme, namely, the variational transform wave method (VTWM), is successfully established to seek the solitary wave solution of the Kadomtsev–Petviashvili model. Furthermore, the fractal solitary solution of fractal Kadomtsev–Petviashvili model is also studied based on the local fractional derivative
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SOME NEW TYPES OF GRONWALL-BELLMAN INEQUALITY ON FRACTAL SET Fractals (IF 4.7) Pub Date : 2024-04-20 GUOTAO WANG, RONG LIU
Gronwall–Bellman-type inequalities provide a very effective way to investigate the qualitative and quantitative properties of solutions of nonlinear integral and differential equations. In recent years, local fractional calculus has attracted the attention of many researchers. In this paper, based on the basic knowledge of local fractional calculus and the method of proving inequality on the set of
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INTELLIGENT EXTRACTION OF COMPLEXITY TYPES IN FRACTAL RESERVOIR AND ITS SIGNIFICANCE TO ESTIMATE TRANSPORT PROPERTY Fractals (IF 4.7) Pub Date : 2024-04-20 YI JIN, BEN ZHAO, YUNHANG YANG, JIABIN DONG, HUIBO SONG, YUNQING TIAN, JIENAN PAN
Fractal pore structure exists widely in natural reservoir and dominates its transport property. For that, more and more effort is devoted to investigate the control mechanism on mass transfer in such a complex and multi-scale system. Apparently, effective characterization of the fractal structure is of fundamental importance. Although the newly emerged concept of complexity assembly clarified the complexity
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BOX DIMENSION OF FRACTAL INTERPOLATION SURFACES WITH VERTICAL SCALING FUNCTION Fractals (IF 4.7) Pub Date : 2024-04-20 LAI JIANG
In this paper, we first present a simple lemma which allows us to estimate the box dimension of graphs of given functions by the associated oscillation sums and oscillation vectors. Then we define vertical scaling matrices of generalized affine fractal interpolation surfaces (FISs). By using these matrices, we establish relationships between oscillation vectors of different levels, which enables us
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ATTACK VULNERABILITY OF FRACTAL SCALE-FREE NETWORK Fractals (IF 4.7) Pub Date : 2024-04-13 FEIYAN GUO, LIN QI, YING FAN
An in-depth analysis of the attack vulnerability of fractal scale-free networks is of great significance for designing robust networks. Previous studies have mainly focused on the impact of fractal property on attack vulnerability of scale-free networks under static node attacks, while we extend the study to the cases of various types of targeted attacks, and explore the relationship between the attack
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A NEW PERSPECTIVE ON THE NONLINEAR DATE–JIMBO–KASHIWARA–MIWA EQUATION IN FRACTAL MEDIA Fractals (IF 4.7) Pub Date : 2024-04-12 JIANSHE SUN
In this paper, we first created a fractal Date–Jimbo–Kashiwara–Miwa (FDJKM) long ripple wave model in a non-smooth boundary or microgravity space recorded. Using fractal semi-inverse skill (FSIS) and fractal traveling wave transformation (FTWT), the fractal variational principle (FVP) was derived, and the strong minimum necessary circumstance was attested with the He Wierstrass function. We have discovered
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A FRACTAL-BASED OIL TRANSPORT MODEL WITH UNCERTAINTY REDUCTION FOR A MULTI-SCALE SHALE PORE SYSTEM Fractals (IF 4.7) Pub Date : 2024-04-10 WENHUI SONG, YUNHU LU, YIHUA GAO, BOWEN YAO, YAN JIN, MIAN CHEN
The challenges of modeling shale oil transport are numerous and include strong solid-fluid interactions, fluid rheology, the multi-scale nature of the pore structure problem, and the different pore types involved. Until now, theoretical studies have not fully considered shale oil transport mechanisms and multi-scale pore structure properties. In this study, we propose a fractal-based oil transport
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NOVEL UNIFIED STABILITY CRITERION FOR FRACTIONAL-ORDER TIME DELAY SYSTEMS WITH STRONG RESISTANCE TO FRACTIONAL ORDERS Fractals (IF 4.7) Pub Date : 2024-04-09 ZHE ZHANG, CHENGHAO XU, YAONAN WANG, JIANQIAO LUO, XU XIAO
In this study, a novel unified stability criterion is first proposed for general fractional-order systems with time delay when the fractional order is from 0 to 1. Such a new unified criterion has the advantage of having an initiative link with the fractional orders. A further advantage is that the corresponding asymptotic stability theorem, derived from the proposed criterion used to analyze the asymptotic
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SOME RESULTS ON BOX DIMENSION ESTIMATION OF FRACTAL CONTINUOUS FUNCTIONS Fractals (IF 4.7) Pub Date : 2024-04-09 HUAI YANG, LULU REN, QIAN ZHENG
In this paper, we explore upper box dimension of continuous functions on [0,1] and their Riemann–Liouville fractional integral. Firstly, by comparing function limits, we prove that the upper box dimension of the Riemann–Liouville fractional order integral image of a continuous function will not exceed 2−υ, the result similar to [Y. S. Liang and W. Y. Su, Fractal dimensions of fractional integral of
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A STUDY OF THE THERMAL EVOLUTION OF PERMEABILITY AND POROSITY OF POROUS ROCKS BASED ON FRACTAL GEOMETRY THEORY Fractals (IF 4.7) Pub Date : 2024-04-09 TONGJUN MIAO, AIMIN CHEN, RICHENG LIU, PENG XU, BOMING YU
The temperature effect on the permeability of porous rocks continues to be a considerable controversy in the area of reservoirs since the thermal expansion of mineral grains exhibits complicated influence on pore geometries in them. To investigate the degree of effect of pore structures on the hydro-thermal coupling process, a study of the thermal evolution of permeability and porosity of porous rocks
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FRACTAL DIMENSIONS FOR THE MIXED (κ,s)-RIEMANN–LIOUVILLE FRACTIONAL INTEGRAL OF BIVARIATE FUNCTIONS Fractals (IF 4.7) Pub Date : 2024-04-09 B. Q. WANG, W. XIAO
The research object of this paper is the mixed (κ,s)-Riemann–Liouville fractional integral of bivariate functions on rectangular regions, which is a natural generalization of the fractional integral of univariate functions. This paper first indicates that the mixed integral still maintains the validity of the classical properties, such as boundedness, continuity and bounded variation. Furthermore,
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ANALYSIS OF THE EFFECT OF VARIOUS MENTAL TASKS ON THE EEG SIGNALS’ COMPLEXITY Fractals (IF 4.7) Pub Date : 2024-04-09 NAJMEH PAKNIYAT, ONDREJ KREJCAR, PETRA MARESOVA, JAMALUDDIN ABDULLAH, HAMIDREZA NAMAZI
Analysis of the brain activity in different mental tasks is an important area of research. We used complexity-based analysis to study the changes in brain activity in four mental tasks: relaxation, Stroop color-word, mirror image recognition, and arithmetic tasks. We used fractal theory, sample entropy, and approximate entropy to analyze the changes in electroencephalogram (EEG) signals between different
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CHAOS THEORY, ADVANCED METAHEURISTIC ALGORITHMS AND THEIR NEWFANGLED DEEP LEARNING ARCHITECTURE OPTIMIZATION APPLICATIONS: A REVIEW Fractals (IF 4.7) Pub Date : 2024-04-05 AKIF AKGUL, YELl̇Z KARACA, MUHAMMED ALI PALA, MURAT ERHAN ÇIMEN, ALI FUAT BOZ, MUSTAFA ZAHID YILDIZ
Metaheuristic techniques are capable of representing optimization frames with their specific theories as well as objective functions owing to their being adjustable and effective in various applications. Through the optimization of deep learning models, metaheuristic algorithms inspired by nature, imitating the behavior of living and non-living beings, have been used for about four decades to solve
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EXACT SOLUTIONS AND BIFURCATION OF A MODIFIED GENERALIZED MULTIDIMENSIONAL FRACTIONAL KADOMTSEV–PETVIASHVILI EQUATION Fractals (IF 4.7) Pub Date : 2024-04-05 MINYUAN LIU, HUI XU, ZENGGUI WANG, GUIYING CHEN
In this paper, we investigate the exact solutions of a modified generalized multidimensional fractional Kadomtsev–Petviashvili (KP) equation by the bifurcation method. First, the equation is converted into a planar dynamical system through fractional complex wave transformation. The phase portraits of the equation and qualitative analysis are presented under different bifurcation conditions. Then,
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SOME ZAGREB-TYPE INDICES OF VICSEK POLYGON GRAPHS Fractals (IF 4.7) Pub Date : 2024-04-05 ZHIQIANG WU, YUMEI XUE, HUIXIA HE, CHENG ZENG, WENJIE WANG
Chemical graph theory plays an essential role in modeling and designing any chemical structure or chemical network. For a (molecular) graph, the Zagreb indices and the Zagreb eccentricity indices are well-known topological indices to describe the structure of a molecule or graph and can be used to predict properties such as the size and number of rings in a molecule, as well as the thermodynamic stability
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VARIATIONAL FORMULATIONS FOR A COUPLED FRACTAL–FRACTIONAL KdV SYSTEM Fractals (IF 4.7) Pub Date : 2024-04-04 YINGZI GUAN, KHALED A. GEPREEL, JI-HUAN HE
Every shallow-water wave propagates along a fractal boundary, and its mathematical model cannot be precisely represented by integer dimensions. In this study, we investigate a coupled fractal–fractional KdV system moving along an irregular boundary within the framework of variational theory, which is commonly employed to derive governing equations. However, not every fractal–fractional differential
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A NEW ROUGH FRACTURE PERMEABILITY MODEL OF COAL WITH INJECTED WATER BASED ON DAMAGED TREE-LIKE BRANCHING NETWORK Fractals (IF 4.7) Pub Date : 2024-04-03 ZHEN LIU, ZHENG LI, HE YANG, JING HAN, MUYAO ZHU, SHUAI DONG, ZEHAN YU
The fracture network structure of coal is very complex, and it has always been a hot issue to characterize the fracture network structure of coal by using a tree-like branching network. In this paper, a new rough fracture permeability model of water injection coal based on a damaged tree-like branching network is proposed. In this model, fractal theory and sine wave model are used to characterize the
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DECODING OF THE EXTRAOCULAR MUSCLES ACTIVATIONS BY COMPLEXITY-BASED ANALYSIS OF ELECTROMYOGRAM (EMG) SIGNALS Fractals (IF 4.7) Pub Date : 2024-04-03 SRIDEVI SRIRAM, KARTHIKEYAN RAJAGOPAL, ONDREJ KREJCAR, HAMIDREZA NAMAZI
The analysis of extraocular muscles’ activation is crucial for understanding eye movement patterns, providing insights into oculomotor control, and contributing to advancements in fields such as vision research, neurology, and biomedical engineering. Ten subjects went through the experiments, including normal watching, blinking, upward and downward movements of eyes, and eye movements to the left and
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RESEARCH ON FRACTAL DIMENSIONS AND THE HÖLDER CONTINUITY OF FRACTAL FUNCTIONS UNDER OPERATIONS Fractals (IF 4.7) Pub Date : 2024-04-01 BINYAN YU, YONGSHUN LIANG
Based on the previous studies, we make further research on how fractal dimensions of graphs of fractal continuous functions under operations change and obtain a series of new results in this paper. Initially, it has been proven that a positive continuous function under unary operations of any nonzero real power and the logarithm taking any positive real number that is not equal to one as the base number
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INVESTIGATION ON CONCRETE MICROSTRUCTURAL EVOLUTION AND SLOPE STABILITY BASED ON COUPLED FRACTAL FLUID–STRUCTURE MODEL Fractals (IF 4.7) Pub Date : 2024-04-01 TINGTING YANG, YANG LIU, GUANNAN LIU, BOMING YU, MINGYAO WEI
Slope instability is a common type of damage in embankment dams. Analyzing its microstructural changes during water transport is beneficial to identify the critical damage point in more detail. To this end, we closely link both diffused water molecule and damaged concrete. On the basis of the original research on fractal theory, the fractal permeability model for the pore system is established. At
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FRACTAL ANALYSIS FOR PERMEABILITY OF MULTIPLE SHALE GAS TRANSPORT MECHANISMS IN ROUGHENED TREE-LIKE NETWORKS Fractals (IF 4.7) Pub Date : 2024-03-27 YIDAN ZHANG, BOQI XIAO, YANBIN WANG, GUOYING ZHANG, YI WANG, HAORAN HU, GONGBO LONG
In this work, a new gas transport model for shale reservoirs is constructed by embedding randomly distributed roughened tree-like bifurcation networks into the matrix porous medium. We constructed apparent permeability models for different shale gas flow mechanisms based on fractal theory, taking into account the effects of relative roughness and surface diffusion. The effects of bifurcation structure
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A NOVEL TRANSFORMER METHOD PRETRAINED WITH MASKED AUTOENCODERS AND FRACTAL DIMENSION FOR DIABETIC RETINOPATHY CLASSIFICATION Fractals (IF 4.7) Pub Date : 2024-03-27 YAOMING YANG, ZHAO ZHA, CHENNAN ZHOU, LIDA ZHANG, SHUXIA QIU, PENG XU
Diabetic retinopathy (DR) is one of the leading causes of blindness in a significant portion of the working population, and its damage on vision is irreversible. Therefore, rapid diagnosis on DR is crucial for saving the patient’s eyesight. Since Transformer shows superior performance in the field of computer vision compared with Convolutional Neural Networks (CNNs), it has been proposed and applied
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3D RENDERING OF THE QUATERNION MANDELBROT SET WITH MEMORY Fractals (IF 4.7) Pub Date : 2024-03-27 RICARDO FARIELLO, PAUL BOURKE, GABRIEL V. S. ABREU
In this paper, we explore the quaternion equivalent of the Mandelbrot set equipped with memory and apply various visualization techniques to the resulting 4-dimensional geometry. Three memory functions have been considered, two that apply a weighted sum to only the previous two terms and one that performs a weighted sum of all previous terms of the series. The visualization includes one or two cutting
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SOME NEW PARAMETRIZED INEQUALITIES ON FRACTAL SET Fractals (IF 4.7) Pub Date : 2024-03-27 HONGYAN XU, ABDELGHANI LAKHDARI, WEDAD SALEH, BADREDDINE MEFTAH
The aim of this study is to examine certain open three-point Newton–Cotes-type inequalities for differentiable generalized s-convex functions on a fractal set. To begin, we introduce a novel parametrized identity involving the relevant formula, which yields various new findings as well as previously established ones. Finally, an example is given to demonstrate the accuracy of the new results and their
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THE (IN)EFFICIENCY OF USA EDUCATION GROUP STOCKS: BEFORE, DURING AND AFTER COVID-19 Fractals (IF 4.7) Pub Date : 2024-03-26 LEONARDO H. S. FERNANDES, JOSÉ P. V. FERNANDES, JOSÉ W. L. SILVA, RANILSON O. A. PAIVA, IBSEN M. B. S. PINTO, FERNANDO H. A. DE ARAÚJO
This paper represents a pioneering effort to investigate multifractal dynamics that exclusively encompass the return time series of USA Education Group Stocks concerning two non-overlapping periods (before, during, and after COVID-19). Given this, we employ the Multifractal Detrended Fluctuations Analysis (MF-DFA). In this sense, we investigate the generalized Hurst exponent h(q) and the Rényi exponent
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SHORTEST PATH DISTANCE AND HAUSDORFF DIMENSION OF SIERPINSKI NETWORKS Fractals (IF 4.7) Pub Date : 2024-03-26 JIAQI FAN, JIAJUN XU, LIFENG XI
In this paper, we will study the geometric structure on the Sierpinski networks which are skeleton networks of a connected self-similar Sierpinski carpet. Under some suitable condition, we figure out that the renormalized shortest path distance is comparable to the planar Manhattan distance, and obtain the Hausdorff dimension of Sierpinski networks.
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APPLICATION OF FRACTIONAL-ORDER INTEGRAL TRANSFORMS IN THE DIAGNOSIS OF ELECTRICAL SYSTEM CONDITIONS Fractals (IF 4.7) Pub Date : 2024-03-26 H. M. CORTÉS CAMPOS, J. F. GÓMEZ-AGUILAR, C. J. ZÚÑIGA-AGUILAR, L. F. AVALOS-RUIZ, J. E. LAVÍN-DELGADO
This paper proposes a methodology for the diagnosis of electrical system conditions using fractional-order integral transforms for feature extraction. This work proposes three feature extraction algorithms using the Fractional Fourier Transform (FRFT), the Fourier Transform combined with the Mittag-Leffler function, and the Wavelet Transform (WT). Each algorithm extracts data from an electrical system
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COMPLEX NETWORKS GENERATED BY A SELF-SIMILAR PLANAR FRACTAL Fractals (IF 4.7) Pub Date : 2024-03-26 QIN WANG, WENJIA MA, KEQIN CUI, QINGCHENG ZENG, LIFENG XI
Many complex networks have scale-free and small-world effects. In this paper, a family of evolving networks is constructed modeled by a non-symmetric self-similar planar fractal, using the encoding method in fractal geometry. Based on the self-similar structure, we study the degree distribution, clustering coefficient and average path length of our evolving network to verify their scale-free and small-world
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ON MULTIPLICATIVE (s,P)-CONVEXITY AND RELATED FRACTIONAL INEQUALITIES WITHIN MULTIPLICATIVE CALCULUS Fractals (IF 4.7) Pub Date : 2024-03-22 YU PENG, TINGSONG DU
In this paper, we propose a fresh conception about convexity, known as the multiplicative (s,P)-convexity. Along with this direction, we research the properties of such type of convexity. In the framework of multiplicative fractional Riemann–Liouville integrals and under the ∗differentiable (s,P)-convexity, we investigate the multiplicative fractional inequalities, including the Hermite–Hadamard- and
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HERMITE–HADAMARD TYPE INEQUALITIES FOR ℏ-CONVEX FUNCTION VIA FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL Fractals (IF 4.7) Pub Date : 2024-03-05 HAIYANG CHENG, DAFANG ZHAO, MEHMET ZEKI SARIKAYA
Fractional q-calculus is considered to be the fractional analogs of q-calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) q-integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving ℏ-convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF q-integral. The results not only
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RESEARCH ON FRACTAL HEAT FLOW CHARACTERIZATION OF FINGER SEAL CONSIDERING THE HEAT TRANSFER EFFECT OF CONTACT GAPS ON ROUGH SURFACES Fractals (IF 4.7) Pub Date : 2024-02-28 JUNJIE LEI, MEIHONG LIU
Finger seal is a new flexible dynamic sealing technology, and its heat transfer characteristics and seepage characteristics are one of the main research hotspots. In this paper, based on the fractal theory, a fractal model of the total thermal conductance of the finger seal considering the heat transfer effect of the contact gap of the rough surface is established, a fractal model of the effective
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A FRACTAL-FRACTIONAL TSUNAMI MODEL CONSIDERING NEAR-SHORE FRACTAL BOUNDARY Fractals (IF 4.7) Pub Date : 2024-02-28 YAN WANG, WEIFAN HOU, KHALED GEPREEL, HONGJU LI
Every fluid problem is greatly affected by its boundary conditions, especially the near-shore seabed could produce an irrevocable harm when a tsunami wave is approaching, and a real-life mathematical model could stave off the worst effect. This paper assumes that the unsmooth seabed is a fractal surface, and fractal-fractional governing equations are established according to physical laws in the fractal
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THREE PROPERTIES OF FRACTAL NETWORKS BASED ON BEDFORD–MCMULLEN CARPET Fractals (IF 4.7) Pub Date : 2024-02-27 JIAN ZHENG, CHENG ZENG, YUMEI XUE, XIAOHAN LI
In this paper, we consider the networks modeled by several self-affine sets based on the Bedford–Mcmullen carpet. We calculate three properties of the networks, including the cumulative degree distribution, the average clustering coefficient and the average path length. We show that such networks have scale-free and small-world effects.
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THE IMPACT OF GLOBAL DYNAMICS ON THE FRACTALS OF A QUADROTOR UNMANNED AERIAL VEHICLE (QUAV) CHAOTIC SYSTEM Fractals (IF 4.7) Pub Date : 2024-02-27 MUHAMMAD MARWAN, MAOAN HAN, YANFEI DAI, MEILAN CAI
In this paper, we have extended the concept of advanced Julia function for the discovery of new type of trajectories existing inside outer and inner wings. A dynamical system based on four rotors, referred to as quadrotor unmanned aerial vehicle (QUAV), is considered for the first time to seek the generation of extra wings using fractal theory. Moreover, we have used Julia and advanced Julia function
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DENG ENTROPY AND INFORMATION DIMENSION FOR COVID-19 AND COMMON PNEUMONIA CLASSIFICATION Fractals (IF 4.7) Pub Date : 2024-02-24 PILAR ORTIZ-VILCHIS, MAYRA ANTONIO-CRUZ, MINGLI LEI, ALDO RAMIREZ-ARELLANO
Motivated by previous authors’ work, where Shannon entropy, box covering and information dimension were applied to quantify pulmonary lesions, this paper extends such a contribution in two fashions: (i) Following the approach to quantify pulmonary lesions with Deng entropy and Deng information dimension obtained through box covering method; (ii) exploiting the Shannon and Deng lesion quantification
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A 3D FRACTAL MODEL COUPLED WITH TRANSPORT AND ACTION MECHANISMS TO PREDICT THE APPARENT PERMEABILITY OF SHALE MATRIX Fractals (IF 4.7) Pub Date : 2024-02-23 SIYUAN WANG, PENG HOU, XIN LIANG, SHANJIE SU, QUANSHENG LIU
The permeability of shale controls gas transport in shale gas reservoirs. The shale has a complex pore structure at the nanoscale and its permeability is affected by multiple transport and action mechanisms. In this study, a 3D fractal model for predicting the apparent gas permeability of shale matrix is presented, accounting for the effects of the transport mechanisms (bulk gas transport and adsorption