Existence, Uniqueness and Stability Analysis for Generalized Φ-Caputo Fractional Boundary Value Problems

This study investigates solutions of a class of boundary value problems involving the Φ-Caputo fractional derivative and the p-Laplacian operator. Through the application of fixed-point theory, we confirm the existence and uniqueness of solutions to nonlinear Φ-Caputo fractional differential equations with the p-Laplacian operator. Moreover, we have demonstrated that this problem is stable in the framework of Ulam–Hyers stability. Our findings enhance the theoretical understanding of fractional differential equations and have potential applications in various scientific and engineering fields. In addition, an illustrative example is provided to support the key insights derived from this research.