System of fractional differential equations with Erdélyi-Kober fractional integral conditions

Abstract

In this paper we study existence and uniqueness of solutions for a system consisting from fractional differential equations of Riemann-Liouville type subject to nonlocal Erdélyi-Kober fractional integral conditions. The existence and uniqueness of solutions is established by Banach’s contraction principle, while the existence of solutions is derived by using Leray-Schauder’s alternative. Examples illustrating our results are also presented.

Keywords

• riemann-liouville fractional derivative
• erdélyi-kober fractional integral
• system
• existence
• uniqueness
• fixed point theorems