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

• Main Authors: Zainab Alsheekhhussain, JinRong Wang, Ahmed Gamal Ibrahim
• Format: Article
• Language: English
• Published: SpringerOpen 2021-07-01
• Series: Advances in Difference Equations
• Subjects: Differential inclusions of fractional order; Sectorial operators; Asymptotically periodic solutions; Caputo fractional derivative; Non-instantaneous impulses
• Online Access: https://doi.org/10.1186/s13662-021-03475-w

Abstract 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 < α < 2 $1<\alpha <2$ 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 , ∞ ) $J=[0,\infty )$ . We adopt the fractional derivative in the sense of the Caputo derivative. We provide three examples illustrating how the results can be applied.