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

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  • Jia Mu
  • Jiecuo Nan
  • Yong Zhou

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.

Suggested Citation

  • Jia Mu & Jiecuo Nan & Yong Zhou, 2020. "Existence and Stability of Square-Mean S-Asymptotically Periodic Solutions to a Fractional Stochastic Diffusion Equation with Fractional Brownian Motion," Complexity, Hindawi, vol. 2020, pages 1-15, October.
    • Handle: RePEc:hin:complx:1045760
    DOI: 10.1155/2020/1045760
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