Asymptotically almost periodic solutions of fractional relaxation inclusions with Caputo derivatives

TL;DR

This paper investigates the existence of asymptotically almost periodic solutions for fractional relaxation inclusions with Caputo derivatives, using advanced mathematical tools and extending previous results to new classes of equations.

Contribution

It introduces novel methods for analyzing asymptotically almost periodic solutions in fractional relaxation inclusions with Stepanov almost periodic coefficients.

Findings

Established existence of solutions under new conditions

Extended analysis to fractional relaxation equations with almost sectorial operators

Provided illustrative examples demonstrating the results

Abstract

In the paper under review, we analyze asymptotically almost periodic solutions for a class of (semilinear) fractional relaxation inclusions with Stepanov almost periodic coefficients. As auxiliary tools, we use subordination principles, fixed point theorems and the well known results on the generation of infinitely differentiable degenerate semigroups with removable singularites at zero. Our results are well illustrated and seem to be not considered elsewhere even for fractional relaxation equations with almost sectorial operators.