Mixed Erdélyi-Kober and Caputo fractional differential equations with nonlocal non-separated boundary conditions

Abstract

In this paper, we investigate a sequential fractional boundary value problem that contains a combination of Erdélyi-Kober and Caputo fractional derivative operators subject to nonlocal, non-separated boundary conditions. We establish the uniqueness of the solution by using Banach's fixed point theorem, while via Krasnosel'skiĭ's fixed-point theorem and Leray-Schauder's nonlinear alternative, we prove the existence results. The obtained results are illustrated by constructed numerical examples.

Keywords

• erdélyi-kober fractional derivative
• caputo fractional derivative
• existence and uniqueness
• fixed point theorems
• nonlocal boundary conditions