A novel multistep generalized differential transform method for solving fractional-order Lü chaotic and hyperchaotic systems

This paper investigates the approximate numerical solutions of the fractional-order Lü chaotic and hyperchaotic systems based on a multistep generalized differential trans- form method (MGDTM). This method has the advantage of giving an analytical form of the solution within each time interval which is not possible using purely numerical techniques. In addition, this paper presents a comparative study between a new scheme and the classical Runge-Kutta method to demonstrate the applicability of the MGDTM. Furthermore, numerical results are presented graphically and reveal that the proposed scheme is an effective, simple and convenient method for solving nonlinear fractional-order chaotic systems with less computational and iteration steps.