Existence, Uniqueness, and Stability of Solutions for Nabla Fractional Difference Equations

Abstract

In this paper, we study a class of nabla fractional difference equations with multipoint summation boundary conditions. We obtain the exact expression of the corresponding Green’s function and deduce some of its properties. Then, we impose some sufficient conditions in order to ensure existence and uniqueness results. Also, we establish some conditions under which the solution to the considered problem is generalized Ulam–Hyers–Rassias stable. In the end, some examples are included in order to illustrate our main results.

Keywords

• nabla fractional difference
• summation conditions
• existence results
• uniqueness result
• stability