Existence of mild solutions to Hilfer fractional evolution equations in Banach space

TL;DR

This paper establishes the existence of mild solutions for Hilfer fractional evolution equations with non-instantaneous impulses in Banach spaces, utilizing semigroup theory and measures of non-compactness.

Contribution

It introduces new existence results for mild solutions to semi-linear Hilfer fractional evolution equations with impulses in Banach spaces.

Findings

Existence of mild solutions proven under certain conditions.

Application of Kuratowski measure of non-compactness in fractional evolution equations.

Use of equicontinuous $C_{0}$-semigroup theory in the analysis.

Abstract

In this paper, we investigate the existence of mild solutions to Hilfer fractional equation of semi-linear evolution with non-instantaneous impulses, using the concepts of equicontinuous $C_{0}$-semigroup and Kuratowski measure of non-compactness in Banach space $\Omega$.