Direct Method for solving Caputo-Favrizio dufferential equation

Abstract

Recently, a new fractical differntial operator has been introduced to get rid of the singularity in the conventional Caputo fractional derivative, which is called the Caputo-Fabrizio fractional operator. In this work, we propose an efficient numerical method based on the predictor-corrector scgeme which reduceds a computational cost by applying an exponential time stepping approach to the memory term. Also the propose method providers an accurate predictor by using known approximations so that it improve the numerical performance. Several numerical illustration have been demonstrated to confirm the efficiency of the proposed method. The proposed numerical scheme provides an important key that a newly introduced operator will be used an appropriate mathematical model to describe may natural phenomena.