| Riemann—Liouville型分数阶微分方程的微分变换方法 |
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| 引用本文： | 叶俊杰,钱德亮. Riemann—Liouville型分数阶微分方程的微分变换方法[J]. 应用数学与计算数学学报, 2009, 23(2): 111-120 |
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| 作者姓名： | 叶俊杰 钱德亮 |
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| 作者单位： | 上海大学数学系,上海,200444 |
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| 基金项目： | 国家自然科学基金，上海大学研究生创新基金 |
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| 摘 要： | 本文在Riemann-Liouville分数阶导数的广义Taylor公式的基础上,建立了求解Riemann-Liouville型分数阶微分方程的微分变换方法.本文所建立的基于Riemann-Liouville分数阶导数微分变换方法给求解Riemann-Liouville分数阶导数的微分方程提供了一种新工具。
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| 关 键 词： | 广义Taylor公式 微分变换方法 序列分数阶导数 Riemann—Liouville 分数阶导数 |
Differential Transform Method for the Fractioanl Differential Equations with Riemann-Liouville Derivative |
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| Ye Junjie,Qian Deliang. Differential Transform Method for the Fractioanl Differential Equations with Riemann-Liouville Derivative[J]. Communication on Applied Mathematics and Computation, 2009, 23(2): 111-120 |
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| Authors: | Ye Junjie Qian Deliang |
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| Affiliation: | Ye Junjie Qian Deliang ( Department of Mathematics, Shanghai University, Shanghai 200444, China) |
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| Abstract: | Based on generalized Taylor's formula involving the Riemann-Liouville fractional derivative, the new differential transformation for the fractional differential equation with Riemann-Liouville derivative is established and applied to solving the equa-tion with Ruemann-Liouville derivative. The illustrative examples show that the derived method is a effective one for solving such a kind of fractional differential equations. |
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| Keywords: | generalized Taylor's formula differential transform method sequential fractional derivative Riemann-Liouville fractional derivative |
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