A New Result for ψ‐Hilfer Fractional Pantograph‐Type Langevin Equation and Inclusions

Abstract

In this paper, we deal with the existence and uniqueness of solution for ψ‐Hilfer Langevin fractional pantograph differential equation and inclusion; these types of pantograph equations are a special class of delay differential equations. The existence and uniqueness results are obtained by making use of the Krasnoselskii fixed‐point theorem and Banach contraction principle, and for the inclusion version, we use the Martelli fixed‐point theorem to get the existence result. In the end, we are giving an example to illustrate our results.