Abstract

In this paper, a new approach of the iterative method is developed to handle nonlinear differential equations of fractional order. For this reason, an efficient modification of iterative method, namely iterative-Laurent method, is introduced based on iterative method and Laurent series expansion. The proposed approach is capable of reducing the size of calculations and easily overcome the difficulty arising in calculating complicated integrals. Furthermore, the new approach is compared with the variational iteration method and Adomian decomposition method in various nonlinear fractional differential equations and the obtained results reveal that the proposed method is more accurate and efficient.

Key words: Fractional differential equations, Iterative method, laurent series expansion, caputo's fractional differential operator.

Abbreviation

VIM, Variational iteration method; ADM, Adomian decomposition method; IM, iterative method; ILM, Iterative- Laurent method.