On coupled Langevin-type fractional differential systems with mixed Erdelyi-Kober and Caputo derivatives

Abstract

This manuscript investigates the existence and uniqueness of solutions for a coupled system of Langevin-type fractional differential equations involving Erdelyi-Kober and Caputo fractional derivatives, subject to non-separated boundary conditions. Uniqueness is established using the Banach contraction principle, while existence results are derived via the Leray–Schauder alternative and Krasnosel'skii’s fixed point theorem. To illustrate the validity and applicability of the theoretical findings, several examples are provided.