Application of the modified differential transform method to fractional oscillators

Purpose: The purpose of this paper is to find a semi-analytic solution to the fractional oscillator equations. In this paper, the authors apply the modified differential transform method to find approximate analytical solutions to fractional oscillators. Design/methodology/approach: The modified differential transform method is used to obtain the solutions of the systems. This approach rests on the recently developed modification of the differential transform method. Some examples are given to illustrate the ability and reliability of the modified differential transform method for solving fractional oscillators. Findings: The main conclusion is that the proposed method is a good way for solving such problems. The results are compared with those obtained by the fourth-order Runge-Kutta method. It is shown that the results reveal that the modified differential transform method in many instances gives better results. Originality/value: The paper demostrates that a hybrid method of differential transform method, Laplace transform and Padé approximations provides approximate solutions of the oscillatory systems.