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

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.The Portuguese Foundation for Science and Technology (FCT) and CIDMA. NSRF via the Program Management Unit for Human Resources & Institutional Development, Research and Innovation.publishe