On Separate Fractional Sum-Difference Equations with n -Point Fractional Sum-Difference Boundary Conditions via Arbitrary Different Fractional Orders

摘要

In this article, we study the existence and uniqueness results for a separate nonlinear Caputo fractional sum-difference equation with fractional difference boundary conditions by using the Banach contraction principle and the Schauder’s fixed point theorem. Our problem contains two nonlinear functions involving fractional difference and fractional sum. Moreover, our problem contains different orders in n + 1 fractional differences and m + 1 fractional sums. Finally, we present an illustrative example.