Existence and uniqueness results of nonlinear hybrid Caputo-Fabrizio fractional differential equations with periodic boundary conditions

Abstract

In this manuscript , we establish the existence and uniqueness of solutions for nonlinear hybrid fractional differential equations involving Caputo-Fabrizio fractional derivatives of order $\varrho\in(0,1)$. The proofs are based on Banach fixed point theorem and some basic concept of Caputo-Fabrizio fractional analysis. As an application, an nontrivial example is given in the last part of this paper to illustrate our theoretical results.