Existence and uniqueness results for coupled system of fractional differential equations with exponential kernel derivatives

Abstract

In the framework of Caputo–Fabrizio derivatives, we study a new coupled system of fractional differential equations of higher orders supplemented with coupled nonlocal boundary conditions. The existence and uniqueness results of the solutions are proved. We consider the classical fixed–point theories due to Banach and Krasnoselskii for the main results. An example illustrating the main results is introduced.

Keywords

• fractional differential equations
• caputo–fabrizio
• coupled system
• existence
• fixed–point theorems