A New Result for ψ-Hilfer Fractional Pantograph-Type Langevin Equation and Inclusions - Hamid Lmou; Khalid Hilal; Ahmed Kajouni (Journal of Mathematics)
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.