On the nonlinear impulsive Ψ–Hilfer fractional differential equations

Abstract

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

Keywords

• Ψ–Hilfer fractional derivative
• fractional differential equations
• impulsive
• nonlocal
• existence and uniqueness
• fixed point theorem