A Generalized System of Fractional Differential Equations of Beam Type: Existence of Solutions and Stability

Abstract

We study the existence of solutions and their Ulam-stability for a coupled system of nonlinear fractional differential equations. The fractional calculus is used by assuming the Caputo fractional derivative, which indicates a good record for applications. Our method is based on the theory of fixed points. As a consequence, two main theorems on the existence of solutions are proved. Some examples are provided to illustrate the applications of the obtained results. Another main result of Ulam-Hyers stability of the solutions of the system is also discussed.