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Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay

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Abstract

This paper studies a class of the fractional stochastic evolution equation with delay. With the aid of the compact semigroup theory and Schauder fixed point theorem, the existence of square-mean S-asymptotically periodic mild solutions is obtained under the situation that the nonlinear functions satisfy certain growth conditions. Moreover, by establishing a new Grönwall integral inequality corresponding to fractional differential equation with delay, the global asymptotic stability of the square-mean S-asymptotically periodic mild solutions are discussed. Finally, an example is given to illustrate our abstract results.

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Acknowledgements

The authors are most grateful to the editor and anonymous referees for the careful reading of the manuscript and valuable suggestions that helped in significantly improving an earlier version of this paper. The first author is partially supported by NNSF of China (No.11871302), China Postdoctoral Science Foundation (No.2020M682140), NSF of Shanxi, China (No.201901D211399) and Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi Province (No.2020L0243).

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Authors and Affiliations

  1. Department of Mathematics, Qinghai Normal University, Xining, 810000, People’s Republic of China

    Qiang Li

  2. Department of Mathematics, Shanxi Normal University, Taiyuan, 030000, People’s Republic of China

    Qiang Li & Xu Wu

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  1. Qiang Li
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  2. Xu Wu
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Li, Q., Wu, X. Existence and asymptotic behavior of square-mean S-asymptotically periodic solutions for fractional stochastic evolution equation with delay. Fract Calc Appl Anal 26, 718–750 (2023). https://doi.org/10.1007/s13540-023-00130-x

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