Analysis of hybrid fractional differential equations with nonlocal boundary conditions and linear perturbations

This research focuses on the study of hybrid fractional differential equations with linear perturbation of the second type. The primary objective of this work is to establish the existence of solutions for the proposed hybrid fractional differential equations. To achieve the desired results, we apply the tools of Banach contraction and Krasnoselskii’s fixed point theorem respectively to derive the conditions for the existence of solutions to the considered problem. Moreover, we developed the conditions for stability analysis of our proposed problem. In addition, the fundamental types of differential inequalities are used to establish the necessary conditions for the minimal and maximal solutions of the underlying hybrid fractional differential equation. Finally, we present illustrative examples to demonstrate the key findings of this study.