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Asymptotic Almost-Periodicity for a Class of Weyl-Like Fractional Difference Equations

Author

Listed:
  • Junfei Cao

    (Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China)

  • Amar Debbouche

    (Department of Mathematics, Guelma University, Guelma 24000, Algeria)

  • Yong Zhou

    (Faculty of Mathematics and Computational Science, Xiangtan University, Xiangtan 411105, China
    Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

This work deal with asymptotic almost-periodicity of mild solutions for a class of difference equations with a Weyl-like fractional difference in Banach space. Based on a combination of a decomposition technique and the Krasnoselskii’s fixed point theorem, we establish some new existence theorems of mild solutions with asymptotic almost-periodicity. Our results extend some related conclusions, since (locally) Lipschitz assumption on the nonlinear perturbation is not needed and with Lipschitz assumption becoming a special case. An example is presented to validate the application of our results.

Suggested Citation

  • Junfei Cao & Amar Debbouche & Yong Zhou, 2019. "Asymptotic Almost-Periodicity for a Class of Weyl-Like Fractional Difference Equations," Mathematics, MDPI, vol. 7(7), pages 1-24, July.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:7:p:592-:d:244790
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