Asymptotically periodic behavior of solutions to fractional non-instantaneous impulsive semilinear differential inclusions with sectorial operators

Advances in Difference Equations

article

Alsheekhhussain, Zainab¹  Wang, JinRong²  Ibrahim, Ahmed Gamal³ 

[1] Department of Mathematics, Faculty of Science, University of Ha’il;Department of Mathematics, Guizhou University;Department of Mathematics and Statistics, College of Science, King Faisal University

关键词: Differential inclusions of fractional order;    Sectorial operators;    Asymptotically periodic solutions;    Caputo fractional derivative;    Non-instantaneous impulses;   

DOI  :  10.1186/s13662-021-03475-w

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we prove two results concerning the existence of S-asymptotically ω-periodic solutions for non-instantaneous impulsive semilinear differential inclusions of order$1<\alpha <2$ and generated by sectorial operators. In the first result, we apply a fixed point theorem for contraction multivalued functions. In the second result, we use a compactness criterion in the space of bounded piecewise continuous functions defined on the unbounded interval$J=[0,\infty )$ . We adopt the fractional derivative in the sense of the Caputo derivative. We provide three examples illustrating how the results can be applied.

【 授权许可】

CC BY