Solutions of the initial value problem for nonlinear fractional ordinary differential equations by the Rach-Adomian-Meyers modified decomposition method

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• 作者：Jun-Sheng Duan^a ; ^{duanjssdu@sina.com} ; ^{duanjs@sit.edu.cn} ; Temuer Chaolu^b ; ^{tmchaolu@shmtu.edu.cn} ; Randolph Rach^c ; ^{tapstrike@triton.net}
• 关键词：Adomian decomposition method ; Modified decomposition method ; Adomian&ndash ; Rach theorem ; Adomian polynomials ; Power series ; Fractional differential equations
• 刊名：Applied Mathematics and Computation
• 出版年：2012
• 期刊代码：7_00963003
• 类别：cp
• 出版时间：1 May, 2012
• 卷：218
• 期：17
• 页码：8370-8392
• 文件大小：706 K

摘要

In this paper we present the generalized Adomian-Rach theorem and the generalized Rach-Adomian-Meyers modified decomposition method for solving multi-order nonlinear fractional ordinary differential equations. We consider different classes of initial value problems for nonlinear fractional ordinary differential equations, including the case of real-valued orders and another case of rational-valued orders, which are solved by the present method. This method can treat any analytic nonlinearity. The coefficients of the solution in the form of a generalized power series are determined by a convenient recurrence scheme, which does not involve integration operations compared with the classic Adomian decomposition method.