Solutions and Stabilities for a 2D− non Homogeneous Lane-Emden Fractional System

Abstract

In this work, we are concerned with a two dimension frac- tional Lane Emden differential system with right hand side depending on an unknown vector function. Using Banach con- traction principle on an appropriate product Banach space, we establish some results on the existence and uniqueness of solu- tions. The existence of at least one solution of the considered problem is also studied. Some notions of Ulam type stabili- ties are presented and illustrated. At the end, an example is discussed.