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A time-fractional superdiffusion wave-like equation with subdiffusion possibly damping term: well-posedness and Mittag-Leffler stability

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Abstract

In this article, we focus on the application of the recent notion of time-fractional derivative developed in Sobolev spaces to the study of well-posedness and stability for a time-fractional wave-like equation with superdiffusion and subdiffusion terms.

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Acknowledgements

M. A. Jorge Silva has been partially supported by the CNPq Grant 309929/2022-9. S. B. Pinheiro has been supported by the regular doctorate scholarship from CAPES-Brazil (PICME), Finance code 001.

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Authors and Affiliations

  1. Departament of Mathematics, State University of Maringá, Maringá, CEP 87020-900, Brazil

    C. L. Frota & S. B. Pinheiro

  2. Departament of Mathematics, State University of Londrina, Londrina, CEP 86057-970, Brazil

    M. A. Jorge Silva

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  1. C. L. Frota
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  2. M. A. Jorge Silva
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Correspondence to C. L. Frota.

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Frota, C.L., Silva, M.A.J. & Pinheiro, S.B. A time-fractional superdiffusion wave-like equation with subdiffusion possibly damping term: well-posedness and Mittag-Leffler stability. Fract Calc Appl Anal 27, 1236–1266 (2024). https://doi.org/10.1007/s13540-024-00249-5

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