On a two-point nonlinear hybrid fractional boundary value problem

We study a nonlinear Caputo type hybrid fractional differential equation subject to a two-point boundary condition. The existence of at least one solution is proven by applying a Burton-type modification of Krasnosel'skii's fixed point theorem. To establish uniqueness, we derive a novel form of Grönwall's inequality and employ it to show that the problem admits a unique solution. In addition, the uniqueness of solutions for the proposed hybrid fractional boundary value problem is further analyzed through Banach's contraction principle. Moreover, the Ulam–Hyers stability of the model is investigated. Finally, illustrative examples are provided to demonstrate the applicability of the theoretical results.