Extremal mild solutions of Hilfer fractional Impulsive systems

TL;DR

This paper extends the monotone iterative technique to Hilfer fractional impulsive systems, establishing existence and uniqueness of solutions using upper and lower solutions and Gronwall inequality.

Contribution

It introduces a novel approach for Hilfer fractional impulsive systems by adapting the monotone iterative method with new conditions on non-compactness.

Findings

Existence of solutions established under new conditions.

Uniqueness of solutions proved for Hilfer fractional impulsive systems.

Method extends previous techniques to a broader class of fractional systems.

Abstract

The well established monotone iterative technique that is used to study the existence and uniqueness of fractional impulsive system is extended to Hilfer fractional order in this paper. The results are derived by using the method of upper and lower solution and Gronwall inequality. Also, conditions on non-compactness of measure is used effectively to prove the main result.