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

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