# On the Nonlinear Impulsive $\Psi$--Hilfer Fractional Differential Equations

## TL;DR

This paper investigates nonlinear $ ext{ extPsi}$-Hilfer impulsive fractional differential equations, deriving solution formulas, establishing existence and uniqueness, extending results to nonlocal cases, and providing applications and examples.

## Contribution

It introduces new solution formulas and existence results for nonlinear $ ext{ extPsi}$-Hilfer impulsive fractional differential equations, including nonlocal extensions.

## Key findings

- Derived explicit solution formulas.
- Proved existence and uniqueness of solutions.
- Extended results to nonlocal impulsive fractional equations.

## Abstract

In this paper, we consider the nonlinear $\Psi$-Hilfer impulsive fractional differential equation. Our main objective is to derive the formula for the solution and examine the existence and uniqueness of results. The acquired results are extended to the nonlocal $\Psi$-Hilfer impulsive fractional differential equation. We gave an applications to the outcomes we procured. Further, examples are provided in support of the results we got.