Hybrid Langevin equations involving ψ-Hilfer fractional-order with nonlocal boundary values

Abstract

In this work, we are interested in studying existence and uniqueness criteria for a class of hybrid ψ-Hilfer Langevin equations of fractional order with multipoint boundary conditions. After specifying the conditions and framework, we prove the existence result using Krasnoselskii's fixed point theorem, and under some additional hypotheses, we prove the uniqueness of the solution using Banach's contraction principle theorem. To support our conclusions from a numerical point of view, we formulate two examples that also illustrate the importance of the main results presented.