Generalized existence and uniqueness results for nonlinear Caputo fractional boundary value problems

In this paper, we study a class of nonlinear fractional boundary value problems involving the Caputo fractional derivative of order $\tau \in (1,2]$. We establish sufficient conditions for the existence and uniqueness of solutions. Our analysis is based on Krasnoselskii's fixed-point theorem and the Banach contraction principle in appropriate Banach spaces. The obtained results not only guarantee the solvability of the proposed equation but also generalize and improve several related results available in the literature. An example is provided in several orders to validate the results.