Existence results for nonlinear hybrid fractional differential equations with generalized [Ψ, Φ]−Caputo-Fabrizio derivative

Abstract

The aim of this paper is to develop the theory of fractional hybrid differential equations with perturbations of second type involving $[\Psi,\Phi]-$Caputo-Fabrizio fractional derivative of an arbitrary order $\nu \in(0,1)$. We demonstrate the existence and uniqueness of solutions for a particular class of nonlinear fractional hybrid differential equations with initial conditions by applying Banach's fixed point theorem and some fundamental tools of $[\Psi,\Phi]-$Caputo-Fabrizio fractional calculus. As an example, a significant case is given to illustrate the utility of our theoretical findings.We also, give  some simulations of solution for the proposed model by applying the Adams Bashford with three steps method