Adomian’s Method Applied to Solve Ordinary and Partial Fractional Differential Equations

doi:10.1007/s12204-017-1846-0

Journal of shanghai Jiaotong University (Science) ›› 2017, Vol. 22 ›› Issue (3): 371-376.doi: 10.1007/s12204-017-1846-0

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Adomian’s Method Applied to Solve Ordinary and Partial Fractional Differential Equations

HAO Lili1,2 (郝丽丽), LI Xiaoyan1* (李晓艳), LIU Song1 (刘松), JIANG Wei1 (蒋威)

(1. Department of Mathematics Science, Anhui University, Hefei 230601, China; 2. Department of Mathematics, East China Normal University, Shanghai 200241, China)
(1. Department of Mathematics Science, Anhui University, Hefei 230601, China; 2. Department of Mathematics, East China Normal University, Shanghai 200241, China)

Online:2017-06-02 Published:2017-06-04
Contact: LI Xiaoyan (李晓艳) E-mail:lxynnfjl@126.com

Abstract

Abstract: This paper presents a method to solve the problems of solutions for integer differential and partial differential equations using the convergence of Adomian’s Method. In this paper, we firstly use the convergence of Adomian’s Method to derive the solutions of high order linear fractional equations, and then the numerical solutions for nonlinear fractional equations. we also get the solutions of two fractional reaction-diffusion equations. We can see the advantage of this method to deal with fractional differential equations.

Key words: fractional calculus| ordinary fractional differential equations| partial fractional differential equations| Adomian’s method

摘要： This paper presents a method to solve the problems of solutions for integer differential and partial differential equations using the convergence of Adomian’s Method. In this paper, we firstly use the convergence of Adomian’s Method to derive the solutions of high order linear fractional equations, and then the numerical solutions for nonlinear fractional equations. we also get the solutions of two fractional reaction-diffusion equations. We can see the advantage of this method to deal with fractional differential equations.

关键词: fractional calculus| ordinary fractional differential equations| partial fractional differential equations| Adomian’s method

CLC Number:

O 175.11

HAO Lili1,2 (郝丽丽), LI Xiaoyan1* (李晓艳), LIU Song1 (刘松), JIANG Wei1 (蒋威). Adomian’s Method Applied to Solve Ordinary and Partial Fractional Differential Equations[J]. Journal of shanghai Jiaotong University (Science), 2017, 22(3): 371-376.

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Adomian’s Method Applied to Solve Ordinary and Partial Fractional Differential Equations

Adomian’s Method Applied to Solve Ordinary and Partial Fractional Differential Equations

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