On the Ulam-Hyers-Rassias stability of two structures of discrete fractional three-point boundary value problems: Existence theory

Abstract

We prove existence and uniqueness of solutions to discrete fractional equations that involve Riemann-Liouville and Caputo fractional derivatives with three-point boundary conditions. The results are obtained by conducting an analysis via the Banach principle and the Brouwer fixed point criterion. Moreover, we prove stability, including Hyers-Ulam and Hyers-Ulam-Rassias type results. Finally, some numerical models are provided to illustrate and validate the theoretical results.

Keywords

• discrete fractional operators
• stability
• existence results
• banach principle