SEQUENTIAL LANGEVIN EQUATIONS INVOLVING A GENERALIZED TYPE OF CAPUTO DERIVATIVES

Abstract

This paper delves into a class of sequential Langevin equations characterized by three φ-Caputo fractional derivatives and a φ-RiemannLiouville integral. By harnessing the power of Schauders and Banachs fixed-point theorems, we reveal the existence, uniqueness, and well-posedness of solutions to these equations. To further strengthen our theoretical framework, we present a numerical example that illustrates our findings.