Existence and Uniqueness in Fractional Boundary Value Problems: A Refined Criterion

This paper is devoted to the study of the existence and uniqueness of solutions for a class of differential problems previously investigated by Laadjal. Our main contribution lies in deriving sharper estimates for the associated Green’s functions and employing Rus’s fixed-point theorem within a suitably defined metric framework. Notably, the conditions under which our results hold are less restrictive, thereby encompassing a wider class of problems for which the existence and uniqueness of solutions can be rigorously guaranteed. This theoretical advancement is supported by numerical evidence presented in the final stage of our analysis. A key strength of the proposed approach is that it does not rely on stringent contraction conditions, which enhances its potential applicability to more general classes of fractional differential systems.