Analysis of Hilfer fractional integro-differential equations with almost sectorial operators

TL;DR

This paper studies nonlocal Hilfer fractional integro-differential equations with almost sectorial operators, proving existence of solutions and analyzing their properties using fixed point theorems and semigroup theory.

Contribution

It introduces new existence results for solutions of these equations and explores solution properties under different semigroup conditions.

Findings

Existence of solutions established via Schauder's fixed point theorem.

Analysis of solution properties based on compactness and noncompactness of semigroups.

An illustrative example demonstrating the theoretical results.

Abstract

We investigate a class of nonlocal integro-differential equations involving Hilfer fractional derivatives and almost sectorial operators. We prove existence results by applying Schauder's fixed point technique. Moreover, we show fundamental properties of the solution representation by discussing two cases related to the associated semigroup. For that, we consider compactness and noncompactness properties, respectively. Furthermore, an example is given to illustrate the obtained theory.