Analysis of a novel Class of Nonlinear Boundary Value Langevin Hybrid Fractional Systems

Abstract

This paper explores the existence and uniqueness of solutions for a novel class of nonlinear boundary value Langevin hybrid fractional integro-differential systems involving the $ (\Upsilon, \,\Lambda) $-order Caputo generalized proportional derivative. Our approach is based on a detailed analysis of the properties of the generalized proportional operator. Using Schauder's and Banach's fixed point theorems, we establish the existence and uniqueness of solutions, respectively. To illustrate and support our main findings, we present a concrete example.