Analysis of Impulsive $\varphi$--Hilfer Fractional Differential Equations

TL;DR

This paper investigates the existence, uniqueness, stability, and dependence of solutions of nonlinear impulsive $\

Contribution

It introduces new results on the analysis of impulsive $\\varphi$--Hilfer fractional differential equations using fixed point theorems and Gronwall inequality.

Findings

Established conditions for existence and uniqueness of solutions.

Proved Ulam--Hyers stability of solutions.

Demonstrated dependence of solutions on initial data and parameters.

Abstract

This paper is concerned with the existence and uniqueness, and Ulam--Hyers stabilities of solutions of nonlinear impulsive $\varphi$--Hilfer fractional differential equations. Further, we investigate the dependence of the solution on the initial conditions, order of derivative and the functions involved in the equations. The outcomes are acquired in the space of weighted piecewise continuous functions by means of fixed point theorems and the generalized version of Gronwall inequality.