Data Dependence and Existence and Uniqueness for Hilfer Nabla Fractional Difference Equations

In the present article, we establish sufficient conditions for the existence of a unique bounded solution using a prominent fixed-point theorem for the non-linear initial value problem involving the recently introduced Hilfer nabla fractional difference operator. { (del(((sic),xi))(x)(alpha) = j(alpha, xi(alpha)), alpha is an element of Nx+1 , [(del(x) (-(-1-t)) (xi))(alpha)](alpha-x) = xi(x) = xi(0) , where 0 < (sic)< 1,0 <= beta <= 1,l =(sic)+ beta - (sic) beta and j : N-x x R-n -> R-n. We also analyze the Ulam- Hyers stability of the considered problem and make some interesting observations on the dependence of its solutions on initial conditions and parameters. Finally, we conclude this article by constructing suitable examples to illustrate the applicability of established results.