Motivated by applications in population models, we consider -asymptotically periodic solution of fractional differential equations with periodic environment forces or asymptotically periodic ones. The system is quasi-monotone, and the existence of positive -asymptotically periodic solution is established by using upper and lower solutions. The sufficient conditions that ensure the uniqueness of positive -asymptotically periodic solution are also established on the basis of theory of sublinear operator. The applications of the general conclusions to classical population models yield the global convergence of positive -asymptotically periodic solution in logistic equation with or without weak Allee effect, and the model of two cooperative populations.

中文翻译：

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分数阶系统的渐近周期解及其在总体模型中的应用


受人口模型中应用的启发，我们考虑具有周期性环境力或渐近周期性力的分数阶微分方程的渐近周期解。该系统是拟单调的，利用上解和下解证明了正渐近周期解的存在性。在次线性算子理论的基础上，还建立了保证正渐近周期解唯一性的充分条件。将一般性结论应用到经典种群模型中，得到了带或不带弱Allee效应的Logistic方程正渐近周期解的全局收敛性，以及两个合作种群的模型。