| 含Riemann-Liouville导数分数阶微分方程比较定理的推广 |
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| 引用本文： | 古传运,郑凤霞.含Riemann-Liouville导数分数阶微分方程比较定理的推广[J].内江师范学院学报,2013,28(6):8-12. |
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| 作者姓名： | 古传运 郑凤霞 |
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| 作者单位： | 四川文理学院数学与财经系,四川 达州,635000 |
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| 基金项目： | 四川文理学院科研资助项目 |
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| 摘 要： | 利用分数阶微分方程与相应的Volterra积分方程的等价性,将含Riemann-Liouville导数的分数阶微分方程比较定理中的阶数α的取值范围由(0,1)推广到(n-1,n),n∈Z+,得到任意分数阶的微分方程比较定理,从而扩大了含Riemann-Liouville导数的分数阶微分方程比较定理的使用范围.
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| 关 键 词： | Riemann-Liouville导数 分数阶微分方程 比较定理 |
The Generalization of Comparison Theorems of Fractional Differential Equations with Riemann-Liouville's Derivative |
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| GU Chuan-yun
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ZHENG Feng-xia.The Generalization of Comparison Theorems of Fractional Differential Equations with Riemann-Liouville's Derivative[J].Journal of Neijiang Teachers College,2013,28(6):8-12. |
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| Authors: | GU Chuan-yun ZHENG Feng-xia |
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| Institution: | (School of Mathematics and Finance-Economics, Sichuan University of Arts and Science, Dazhou, Sichuan 635000 ,China) |
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| Abstract: | Abstract： By use of the equivalence between the fractional differential equations and the corresponding Volterra integral equations, the range of the order a of the comparison theorem is extended from a E （0,1） to a （n-1,n）,n∈Z＋, , so that the comparison theorem for any arbitrary fractional order differential equations is obtained and the application scope of this theorem is enlarged. |
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| Keywords: | Riemann-Liouville’s derivative fractional differential equations comparison theorem generalization |
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