Existence of asymptotic almost automorphic solutions of fractional integro differential equations with non local conditions

TL;DR

This paper investigates the existence of asymptotic almost automorphic solutions for fractional integro-differential equations using fixed point theorems, considering cases with and without Lipschitz conditions, supported by illustrative examples.

Contribution

It establishes new existence results for asymptotic almost automorphic solutions of fractional integro-differential equations under broad conditions.

Findings

Existence of solutions proven with fixed point theorems

Results hold with and without Lipschitz conditions

Examples illustrate the theoretical findings

Abstract

This paper deals with the existence of asymptotic almost automorphic solution of fractional integro differential equation. We prove the result by using fixed point theorems. We show the result with Lipschitz condition and without Lipschitz condition on the forcing term. At the end examples have been given to illustrate the analytical findings.