Dhage iterative technique for IVPs of nonlinear Caputo fractional functional ordinary differential equations

Abstract

The aim of this paper is to prove an existence and approximation of solution for a nonlinear hybrid Caputo fractional functional differential equation by developing an algorithm via Dhage iteration method embodied in the hybrid fixed point theorems of Dhage. We construct a sequence of successive approximations based on the algorithm for the considered Caputo fractional functional differential equation with initial condition and it is shown that the sequence converges to solution of the nonlinear differential problem. The results are proved under weaker partial Lipschitz and partial compactness type conditions in a partially ordered Banach space. A couple of numerical examples are also provided to illustrate the abstract results of this paper.