A novel approach on the sequential type ψ-Hilfer pantograph fractional differential equation with boundary conditions

Abstract

Abstract This article investigates sufficient conditions for the existence and uniqueness of solutions to the ψ-Hilfer sequential type pantograph fractional boundary value problem. Considering the system depends on a lower-order fractional derivative of an unknown function, the study is carried out in a special working space. Standard fixed point theorems such as the Banach contraction principle and Krasnosel’skii’s fixed point theorem are applied to prove the uniqueness and the existence of a solution, respectively. Finally, an example demonstrating our results with numerical simulations is presented.

Keywords

• Pantograph fractional differential equation
• ψ-Hilfer fractional derivative
• Fixed point theory
• Existence and uniqueness