Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion

Jia Mu, Jiecuo Nan and Yong Zhou

Complexity, 2020, vol. 2020, 1-15

Abstract:

In this paper, a generalized Gronwall inequality is demonstrated, playing an important role in the study of fractional differential equations. In addition, with the fixed-point theorem and the properties of Mittag–Leffler functions, some results of the existence as well as asymptotic stability of square-mean S -asymptotically periodic solutions to a fractional stochastic diffusion equation with fractional Brownian motion are obtained. In the end, an example of numerical simulation is given to illustrate the effectiveness of our theory results.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:complx:1045760

DOI: 10.1155/2020/1045760

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