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一类非线性分数阶微分方程组的爆破解 被引量：2

Blowing-up Solutions of a Type of Nonlinear System of Fractional Differential Equations
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摘要 用Laplace变换法研究一类时间分数阶非线性微分方程组,得到了与其等价的积分方程组.结果表明,积分方程组存在局部解.用Hlder不等式估计非线性时间方程组,得到了该方程组具有有限时间的爆破解. The authors focused on the study of a type of nonlinear system of time-fractional differential equations,and obtainsed the system of the integral equations which is equivalent to the system of nonlinear partial differential equations with time-fractional derivative via the approach of Laplace transformation,and proved the existence of local solutions to the system of the integral equations.In addition,we investigated the blowing-up solutions to the nonlinear system of fractional differential equations using Hlder＇s inequality,and obtained the blowing-up solution of equation set in a finite time.
作者 代群 李辉来
机构地区 吉林大学数学研究所
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2012年第1期1-5,共5页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:10771085)
关键词 分数阶微分方程 爆破解 LAPLACE变换 方程组 fractional differential equation blowing-up solution Laplace transformation system
分类号 O175.1 [理学—基础数学]
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参考文献13

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同被引文献12

  • 1GENG Xiang-guo, CAO Ce-wen. Quasi-periodic solution of the (2 + 1 )-dimensional modified Korteweg-de equation[ J]. Physics Letters A, 1999, 261:289 -296.
  • 2ZHANG J S, WU Y T, LI X M. Quasi-periodic solution of the (2 + 1 ) -dimensional Boussinesq-Burgers soliton equation [ J ]. Journal of Physics A, 2003, 319:213 -232.
  • 3LI Y S, MAW X, ZHANG J E. Darboux transformations of classical boussinesq system and its new solutions[ J ]. Physics Letters A, 2000, 275 60 - 66.
  • 4LIU Ping, ZHANG Jin-shun. Darboux transformations of Broer-Kaup system and its odd-soliton solutions[ J]. Journal of Southwest China Normal U niversity, 2006 ( 5 ) :31 - 36.
  • 5WU Yongyan, WANG Chun, LIAO Shijun. Solving the One Loop Soliton Solution of the Vakhnenko Equation by Means of the Homotopy Analysis Method [J]. Chaos, Solitons ~ Fractals, 2004, 23(5) : 1733-1740.
  • 6SONG I.ina, ZHANG Hongqing. Application of Homotopy Analysis Method to Fractional KdV-Burgers- Kuramoto Equation[J].Phys Lett A, 2007, 367(1/2): 88-94.
  • 7Lesnic D. The Decomposition Method for Initial Value Problems [J]. Appl Math Comput, 2006, 181(1): 206-213.
  • 8Jafari H, Daftardar-Gejji V. Solving a System of Nonlinear Fractional Differential Equations Using Adomain Decomposition [J]. J Comput Appl Math, 2006, 196(2): 644-651.
  • 9Odibat Z, Momani S. Modified Homotopy Perturbation Method: Application to Quadratic Riccati Differential Equation of Fractional Order[J]. Chaos, Solitons & Fractals, 2008, 36(1) : 167-174.
  • 10Momani S, Odibat Z. Numerical Comparison of Methods for Solving Linear Differential Equations of Fractional Order [J]. Chaos, Solitons & Fractals, 2007, 31(5) : 1248-1255.

引证文献2

二级引证文献5

吉林大学学报（理学版）
2012年 第1期

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