A FINITE DIFFERENCE SCHEME FOR CAPUTO-FABRIZIO FRACTIONAL DIFFERENTIAL EQUATIONS

In this work, we consider a new fractional derivative with nonsingular kernel introduced by Caputo-Fabrizio (CF) and propose a finite difference method for computing the CF fractional derivatives. Based on an iterative technique, we can reduce the computational complexity from O(J(2)N) to O(JN), and the corresponding storage will be cut down from O(JN) to O (N), which makes the computation much more efficient. Besides, by adopting piece-wise Lagrange polynomials of degrees 1, 2, and 3, we derive the second, third, and fourth order discretization formulas respectively. The error analysis and numerical experiments are carefully provided for the validation of the accuracy and efficiency of the presented method.