On a Self-Adjoint Fractional Nabla Finite Dierence Equation with Initial Value Condition

Abstract. By using discrete fractional calculus, we investigate the existence of solutions for a self-adjoint nite Nabla fractional dierence equation on the time scale Nb a+1 via initial boundary conditions. Also, we check some conditions for uniqueness of solution of the problem. For nding the solution, we use the Green function which dened by using the Cauchy function. The principle of contraction mapping also plays an essential role in the existence of the solution. We provided two examples, a gure and numerical results to illustrate our main result. AMS Subject Classication: 34A12; 65L12.