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分数阶微分方程的比较定理 被引量:17

Comparison Theorems of Fractional Differential Equations
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摘要 本文给出了非线性Riemann-Liouville分数阶微分方程和Caputo分数阶微分方程与相应的非线性Volterra积分方程的等价性,并在此基础上建立了分数阶微分方程的比较定理. In this paper, we show the equivalence between the nonlinear Riemann- Liouville and Caputo fractional differential equations and the Volterra integral equations, respectively. And we also establish the comparison theorems of the fractional differential equations.
出处 《应用数学与计算数学学报》 2009年第1期97-103,共7页 Communication on Applied Mathematics and Computation
基金 国家自然科学基金(10872119)部分资助
关键词 Riemann—Liouville导数 CAPUTO导数 分数阶比较定理 Riemann-Liouville fractional derivative, Caputo fractional derivative, fractional comparison theorems
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参考文献9

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同被引文献78

  • 1袁晓,张红雨,虞厥邦.分数导数与数字微分器设计[J].电子学报,2004,32(10):1658-1665. 被引量:47
  • 2段俊生.含Caputo分数阶导数的分数阶微分方程[J].天津轻工业学院学报,2003,18(B12):21-24. 被引量:5
  • 3Haitao Qi,Hui Jin.Unsteady rotating flows of a viscoelastic fluid with the fractional Maxwell model between coaxial cylinders[J].Acta Mechanica Sinica,2006,22(4):301-305. 被引量:9
  • 4张慧琛,魏毅强.关于一类分形函数的分数阶微积分函数[J].太原科技大学学报,2006,27(6):457-458. 被引量:3
  • 5Bai Zhanbing,Lu Haishen.Positive solutions for boundary value problem of nonlinear fractional differential equation[J].J.Math.Anal.Appl.,2005,311:495-505.
  • 6Zhang Shuqin.Positive solutions to singular boundary value problem for nonlinear fractional differential equation[J].Computer and Mathematics with Applications,2010,59:1 300-1 309.
  • 7Xu Xiaojie,Jiang Daqing,Yuan Chengjun.Multiple positive solutions for boundary value problem of a nonlinear fractional differential equation[J].Nonlinear Analysis,2009,71:4 676-4 688.
  • 8Bai Zhanbing,Lü Haishen.Positive solutions for boundary value problem of nonlinear fractional differential equation[J].J.Math.Anal.Appl.,2005,311:495-505.
  • 9Zhang Shuqin.Positive solutions to singular boundary value problem for nonlinear fractional differential equation[J].Computer and Mathematics with Applications,2010,59:1300-1309.
  • 10Xu Xiaojie,Jiang Daqing,Yuan Chengjun.Multiple positive solutions for boundary value problem of a nonlinear fractional differential equation[J].Nonlinear Analysis,2009,71:4676-4688.

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