Ulam Stability for A Singular Fractional $ 2D$ Nonlinear System

Abstract

In this paper, we study a singular fractional $2D$ nonlinear system. We investigate the existence and uniqueness of solutions in addition to the existence of at least one solution by means of Schauder fixed point theorem, and the contraction mapping principle. Moreover, we define and study the Ulam-Hyers stability and the generalized Ulam-Hyers stability of solutions for such systems. Some applications are presented to illustrate our main results.