When real-world systems like sensor networks or controllers face small disturbances, do their discrete fractional models stay reliable? We tackle this for a critical but unstudied problem: discrete delta fractional equations with summation multipoint boundary conditions (SMBCs). First, we build the mathematical foundation-the Green's function-to prove solutions exist and are unique under Lipschitz conditions. Crucially, we show these solutions are Ulam-Hyers-Rassias stable: even when perturbed, they stay close to the true solution, with explicit guarantees for both uniform and varying disturbances. Testing this on a nonlinear system and a thermal sensor model confirms real-world resilience. This work bridges abstract fractional calculus with engineering robustness, giving designers confidence to deploy these models in next-generation technologies.
Mohammed et al. (Tue,) studied this question.