Mild and strong solutions for Hilfer evolution equation

TL;DR

This paper studies the existence and uniqueness of solutions to fractional evolution equations involving Hilfer derivatives, using fixed point theorems and inequalities to establish rigorous results.

Contribution

It introduces new results on mild and strong solutions for Hilfer fractional evolution equations, expanding the theoretical understanding in this area.

Findings

Proved existence of mild solutions.

Established uniqueness of strong solutions.

Applied fixed point theorem and Gronwall inequality.

Abstract

In this paper, we investigate the existence and uniqueness of mild and strong solutions of fractional semilinear evolution equations in the Hilfer sense, by means of Banach fixed point theorem and the Gronwall inequality.