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一类广义分数阶时间迟滞微分方程的一些结果 被引量：1

Some results of a generalized fractional order time-delay equation
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摘要 研究一类更广义的分数阶时间迟滞微分方程,证明了此方程的解的存在唯一性以及解的连续性,分别运用步长法和Laplace变换法得出了方程的解.在此基础上,得出了此类方程有限稳定的一个充分条件. In this paper,a generalized fractional order time-delay equation was considerd. The existence and uniqueness of the solution of the equation was proved,and the solution was also continuous in the domain. We separately apply the step method and Laplace transform method to obtain the solution of the equation,further more,a sufficient condition of finite time stability of the equation was gotten.
作者 魏谞婷 卢旋珠
机构地区 福州大学数学与计算机科学学院
出处 《福州大学学报（自然科学版）》 CAS CSCD 北大核心 2010年第2期166-171,共6页 Journal of Fuzhou University(Natural Science Edition)
基金 福建省教育厅科研资助项目(JB07018)
关键词 微分方程 分数阶导数 步长法 LAPLACE变换 有限稳定性 differential equation fractional order derivative steps method Laplace transform method finite time stability
分类号 O15 [理学—基础数学]
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参考文献9

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同被引文献16

  • 1DAS S, GUPTA P K, VISHAL K. Approximate approach to the Das model of fractional logistic population growth [J]. Appl Appl Math, 2010, 5(10) :1702 -1708.
  • 2EL-SAYED A M A, EL-MESIRY A E M, EL-SAKA H A A. On the fractional-order logistic equation [ J ]. Appl Math Lett, 2007, 20:817 -823.
  • 3ABBAS S, BANERJEE M, MOMANI S. Dynamical anal- ysis of fractional-order modified logistic model [J]. Com- put Math Appl, 2011, 62:1098 - 1104.
  • 4EL-SAYED A M A, EL-SAKA It A A, EL-MAGHPtABI E M. On the fractional-order logistic equation with two different delays [J]. Z Naturforsch, 2011, 66a: 1 -5.
  • 5SWEILAM N H, KHADER M M, MAHDY A M S. Nu- merical studies for fractional-order logistic differential e- quation with two different delays [ J ]. J Appl Math, 2012, ID 764894 : 1 - 14.
  • 6SWEILAM N H, KHADER M M, MAHDY A M S. Nu- merical studies for solving fractional-order logistic equa- tion[J]. lnt J Pure Appl Math, 2012, 78:1199 - 1210.
  • 7ZHANG X Y. Some results of linear fractional order time-delay system [ J ]. Appl Math Comput, 2008, 197:407 -411.
  • 8DENG W H, LI C P, LU J H. Stability analysis of line- ar fractional differential system with multiple time delays [J]. Nonlinear Dynam, 2007, 48:409-416.
  • 9KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equation [ M]. New York: Elsevier, 2006.
  • 10BHALEKAR S, DAFTARDAR-GEJJI V. A predictor- corrector scheme for solving nonlinear delay differential equations of fractional order [ J ]. J Fract Calc Appl, 2011, 6: 1-9.

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福州大学学报（自然科学版）
2010年 第2期

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