EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR A DISCRETE FRACTIONAL BOUNDARY VALUE PROBLEM

Abstract

Abstract: This present work discusses existence and uniqueness of solutions for the following discrete fractional antiperiodic boundary value problem of the form C 0 ∆ α kx(k) = f (k + α− 1, x(k + α− 1)) , for k ∈ [0, l + 2]N0 = {0, 1, ..., l + 2}, with boundary conditions x(α − 3) = −x(α+ l), ∆x(α−3) = −∆x(α+ l), ∆2x(α−3) = −∆2x(α+ l), where f : [α− 2, α+l]Nα−2×R → R is continuous and C 0 ∆ α k is the Caputo fractional difference operator with order 2 < α ≤ 3. Finally, the main results are illustrated by suitable examples.