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一类具有初边值条件的非线性分数阶微分方程组解的存在性与唯一性 被引量：1

Existence and Uniqueness for a Coupled System of Nonlinear Fractional Differential Equations with Initial Value Conditions
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摘要 考虑一类具有初边值条件的耦合非线性分数阶微分方程组解的存在性与唯一性问题,应用Schauder和Banach不动点定理得到了此类方程组解的存在性与唯一性条件. We studied a coupled system of nonlinear fractional equations with initial value condition and got the existence and uniqueness of it by means of the Schauder fixed point theorem and Banach fixed point theorem.
作者 李雪梅 代群 李辉来
机构地区 吉林大学数学学院 长春理工大学理学院
出处 《吉林大学学报（理学版）》 CAS CSCD 北大核心 2015年第3期363-366,共4页 Journal of Jilin University:Science Edition
基金 国家自然科学基金(批准号:11271154)
关键词 耦合方程组 分数阶微分方程 存在性 唯一性 SCHAUDER不动点定理 BANACH不动点定理 coupled system fractional differential equations existence uniqueness Sehauder fixedpoint theorem Banach fixed point theorem
分类号 O175.08 [理学—基础数学]
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参考文献10

  • 1BAI Zhanbing,LU Haishen. Positive Solutions for Boundary Value Problems of Nonlinear Fractional DifferentialEquations [J]. Math Anal Appl, 2005,311(2) : 495-505.
  • 2CHANG Yongkai, Nieto J J. Some New Existence Results for Fractional Differential Inclusions with BoundaryConditions [J]. Math Comput Modelling, 2009,49(3/4) : 605-609.
  • 3DENG Weihua. Numerical Algorithm for the Time Fractional Fokker-Planck Equation [J]. J Comput Phys,2007, 227(2) : 1510-1522.
  • 4BAI Chuanzhi,FANG Jinxuan. The Existence of a Positive Solution for a Singular Coupled System of NonlinearFractional Differential Equations [J]_ Appl Math Comput, 2004 f 150(3) : 611-621.
  • 5CHEN Yong,AN Hongli. Numerical Solutions of Coupled Burgers Equations with Time- and Space-FractionalDerivatives [J], Appl Math Comput, 2008,200(1) : 87-95.
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同被引文献8

  • 1Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations.. Vol. 204 [M]//North-Holland Mathematics Studies. Amsterdam: Elsevier Science Limited, 2006.
  • 2Sabatier J, Agrawal O P, Machado J A. Advances in Fractional Calculus [M]//Theoretical Developments and Applications in Physics and Engineering. New York: Springer, 2007.
  • 3WEI Zhongli, LI Qingdong, CHE Junling. Initial Value Problems for Fractional Ditterentlal Equatlons Involving Riemann-Liouville Sequential Fractional Derivative [J]. J Math Anal Appl, 2010, 367(1): 260-272.
  • 4WANG Guotao, Agarwal R P, Cabada A. Existence Results and the Monotone Iterative Technique for Systems of Nonlinear Fractional Differential Equations [J]. Appl Math Lett, 2012, 25(6): 1019-1024.
  • 5LIU Zhenhai, SUN Jihua. Nonlinear Boundary Value Problems of Fractional Differential Systems [J]. Comput Math Appl, 2012, 64(4): 463-475.
  • 6Podlubny I. Geometric and Physical Interpretation of Fractional Integration and Fractional Differentiation [J]. Fract Calc Appl Anal, 2002, 5(4): 367-386.
  • 7BAI Zhanbing, QIU Tingting. Existence of Positive Solution for Singular Fractional Differential Equation [J]. Appl Math Comput, 2009, 215(7): 2761-2767.
  • 8代群,刘素莉,李辉来.非线性分数阶微分方程特征值问题正解的存在性[J].吉林大学学报（理学版）,2015,53(1):1-4. 被引量：2

引证文献1

吉林大学学报（理学版）
2015年 第3期

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