An application to a system of $(k,\rho)$-fractional Hilfer integral equations via a measure of noncompactness

TL;DR

This paper extends Darbo's fixed point theorem using measure of noncompactness to establish the existence of solutions for a system of $(k, ho)$-fractional Hilfer integral equations, with an illustrative example.

Contribution

It generalizes Darbo's fixed point theorem with $ ext{H}$-class mappings and applies it to solve fractional Hilfer integral equations for the first time.

Findings

Established a solvability result for the system of fractional equations.

Provided an example demonstrating the applicability of the theoretical results.

Extended the fixed point theorem to a broader class of mappings.

Abstract

In our study, Darbo's fixed point theorem(DFPT) has been extended and generalized using $\mathbb{H}$-class mappings and the measure of noncompactness. Utilizing this Darbo-type theorem, we provided a solvability result for a system of a $(k,\rho)$-fractional Hilfer integral equations, accompanied by an appropriate example to illustrate the findings.