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

Abstract

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.

Keywords

• Differential inclusions of fractional order
• Sectorial operators
• Asymptotically periodic solutions
• Caputo fractional derivative
• Non-instantaneous impulses