Mathematical Analysis of Caputo–Hadamard Hybrid Fractional Equations with Quadratic Perturbations

Abstract

This paper studies a hybrid fractional differential equation with Caputo-Hadamard derivatives. Using Banach's and Krasnoselskii's fixed-point theorems, we prove existence and uniqueness results under Dirichlet boundary conditions. The hybrid term and nonlinearity are analyzed, and an example illustrates the theory. Our work generalizes Hadamard-type problems to Caputo–Hadamard operators, enabling broader applications. Future research directions are briefly discussed.