Existence and uniqueness of non-periodic solutions to boundary value problems for discrete fractional difference equations with uncertainty

Abstract

In this study, we introduce discrete interval fractional difference equations subject to non-periodic boundary conditions. We obtain two types of solutions for these problems under the generalized Hukuhara difference. Then, we present the explicit expressions of each type of solutions for the convenience of applicability. Further, we investigate the necessary and sufficient conditions which guarantee the existence and uniqueness of a non-periodic solution of each specific type by applying the Banach contraction mapping principle. Finally, we provide an example in order to illustrate the main result.