New Results on the Stability and Existence of Langevin Fractional Differential Equations with Boundary Conditions

This manuscript aims to establish the existence, uniqueness, and stability of solutions for Langevin fractional differential equations involving the generalized Liouville-Caputo derivative. Using a novel approach, we derive existence and uniqueness results through fixed-point theorems, extending and generalizing several existing findings in the literature. To demonstrate the applicability of our results, we provide a practical example that validates the theoretical framework.