Spectral method for solving fractal fractional differential equations

Abstract

Lately introduced fractal fractional Caputo - Fabrizio operator. By substituting the single kernel at the classic derivative of fractal fractional Caputo with the ordinary kernel This modern operator was derived. We introduce some beneficial characteristics relied on the qualifier of fractal fractional Caputo - Fabrizio. Here, we extend Caputo-Fabrizio for nonlinear fractal fractional differential equations. We apply Legendre operational matrix relied on this modern operator and then, we employ it to solve the differential equations determined in the sense of fractal fractional Caputo-Fabrizio. To show the simplicity and precision of the suggested technicality Some numerical examples are given.