﻿ 一类时间分数阶偏微分方程的同伦分析Sumudu变换解法 Homotopy Analysis Sumudu Transform Method for Solving a Class of Time Fractional Partial Differential Equations

Pure Mathematics
Vol.07 No.04(2017), Article ID:21403,12 pages
10.12677/PM.2017.74042

Homotopy Analysis Sumudu Transform Method for Solving a Class of Time Fractional Partial Differential Equations

Bohui Yang, Xindong Zhang*

College of Mathematics Sciences, Xinjiang Normal University, Urumqi Xinjiang

Received: Jun. 29th, 2017; accepted: Jul. 14th, 2017; published: Jul. 19th, 2017

ABSTRACT

In this article we have applied homotopy analysis Sumudu transform method (HASTM) to solve a class of time Fractional partial differential equations (ACFPDEs) with time fractional derivative in Caputo sense. Finally, the accuracy and simplicity of the method are illustrated by the calculation of specific examples.

Keywords:Time Fractional Partial Differential Equation, Sumudu Transform, Homotopy Analysis

1. 引言

2. 预备知识

Mittag-Leffler函数的一些特殊例子如下：

1、

2、

3. 同伦分析Sumudu变换方法的基本思想

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

4. 数值算例

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

(23)

(24)

(25)

，将用到以下解决方案：

(26)

(27)

(28)

(29)

(30)

(31)

(32)

(33)

(34)

(35)

，方程(34)的精确解为：

(36)

(37)

(38)

(39)

，将用到以下解决方案：

(40)

5 结论

Homotopy Analysis Sumudu Transform Method for Solving a Class of Time Fractional Partial Differential Equations[J]. 理论数学, 2017, 07(04): 322-333. http://dx.doi.org/10.12677/PM.2017.74042

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