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S-Asymptotically Periodic Solutions for Time-Space Fractional Evolution Equation

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Abstract

This paper discusses the abstract time-space fractional evolution equation with the Caputo derivative of order \(\alpha \in (0,1)\) and fractional power operator \(-A^{\beta }\), \(\beta \in (0,1)\), where \(-A\) generates a \(C_{0}\)-semigroup on a Banach space. The compactness and exponential stability of the semigroup which is generated by fractional power operator \(-A^{\beta }\) are investigated. With the aid of the properties of the semigroup, the existence and global asymptotic behavior of S-asymptotically periodic solutions are obtained by some fixed point theorems and related inequalities. An example to the time-space fractional diffusion equation with fractional Laplacian will be shown.

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Funding

This work was supported by NNSF of China (11871302) and NSF of Shanxi, China (201901D211399).

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Authors and Affiliations

  1. School of Mathematical Sciences, Qufu Normal University, Qufu, 273165, People’s Republic of China

    Qiang Li & Lishan Liu

  2. Department of Mathematics, Shanxi Normal University, Linfen, 041000, People’s Republic of China

    Qiang Li & Mei Wei

  3. Department of Mathematics, Northwest Normal University, Lanzhou, 730070, People’s Republic of China

    Mei Wei

Authors
  1. Qiang Li
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  2. Lishan Liu
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  3. Mei Wei
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QL carried out the first draft of this manuscript. All authors read and approved the final manuscript.

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Correspondence to Lishan Liu.

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Research supported by NNSF of China (no. 11871302) and NSF of Shanxi, China (no. 201901D211399).

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Li, Q., Liu, L. & Wei, M. S-Asymptotically Periodic Solutions for Time-Space Fractional Evolution Equation. Mediterr. J. Math. 18, 126 (2021). https://doi.org/10.1007/s00009-021-01770-0

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  • DOI: https://doi.org/10.1007/s00009-021-01770-0

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