A robust operational matrix of nonsingular derivative to solve fractional variable-order differential equations

Currently, a study has come out with a novel class of differential operators using fractional-order and variable-order fractal Atangana-Baleanu derivative, which in turn, became the source of inspiration for new class of differential equations. The aim of this paper is to apply the operation matrix to get numerical solutions to this new class of differential equations and help us to simplify the problem and transform it into a system of an algebraic equation. This method is applied to solve two types, linear and nonlinear of fractal differential equations. Some numerical examples are given to display the simplicity and accuracy of the proposed technique and compare it with the predictor-corrector and mixture two-step Lagrange polynomial and the fundamental theorem of fractional calculus methods.