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

Junfei Cao, Amar Debbouche and Yong Zhou
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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

Mathematics, 2019, vol. 7, issue 7, 1-24

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.

Keywords: asymptotically almost-periodic sequence; Weyl-like fractional difference; Fractional difference equation; Krasnoselskii’s fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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