Existence Theorems for Hybrid Fractional Differential Equations with ψ -Weighted Caputo–Fabrizio Derivatives

Abstract

In this study, two classes of hybrid boundary value problems involving $\psi$ -weighted Caputo–Fabrizio fractional derivatives are considered. Based on the properties of the given operator, we construct the hybrid fractional integral equations corresponding to the hybrid fractional differential equations. Then, we establish and extend the existence theory for given problems in the class of continuous functions by Dhage’s fixed point theory. Furthermore, as special cases, we offer further analogous and comparable conclusions. Finally, we give two examples as applications to illustrate and validate the results.