Ulam-Hyers stability for impulsive fractional differential equations in nonreflexive Banach spaces

This paper investigates the existence, uniqueness, and Ulam–Hyers stability of solutions for a class of impulsive multi-term fractional differential equations in nonreflexive Banach spaces. The considered system is formulated in the sense of Caputo fractional derivatives with respect to an increasing function and incorporates nonlinear boundary conditions together with impulsive effects. By transforming the given problem into an equivalent integral equation, sufficient conditions ensuring the existence and uniqueness of solutions are derived via Banach’s fixed point theorem. Furthermore, the Ulam–Hyers stability of the proposed model is established, guaranteeing that approximate solutions remain uniformly close to the exact solution under suitable conditions. The obtained results generalize and extend several existing contributions in the literature on fractional differential equations by including impulsive dynamics and the setting of nonreflexive Banach spaces. Finally, illustrative examples are presented to confirm the applicability and effectiveness of the theoretical results.