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一类具有Riemann-Liouville分数阶积分条件的分数阶微分方程边值问题 被引量：2

Boundary value problem of a class of fractional differential equation with Riemann-Liouville fractional integral conditions
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摘要 研究了一类具有Riemann-Liouville分数阶积分条件的新分数阶微分方程边值问题,其非线性项包含Caputo型分数阶导数.将该问题转化为等价的积分方程,应用Leray-Schauder不动点定理结合一个范数形式的新不等式,获得了解的存在性充分条件,推广和改进了已有的结果,并给出了应用实例. A class of boundary value problem of fractional differential equation with Riemann-Liouville fractional integral conditions is investigated, which involves the Caputo fractional derivative in nonlinear terms and can be reduced to the equivalent integral equation. By using Leray-Schauder fixed point theory combined with a new inequality of norm form, some sufficient conditions on the exitence of solution for boundary value problem are established. Some known results are extended and improved. An example is given to illustrate the application of the result.
作者 李耀红 张海燕
机构地区 宿州学院数学与统计学院
出处 《高校应用数学学报（A辑）》 CSCD 北大核心 2014年第1期24-30,共7页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
基金 安徽省教育厅自然科学研究重点项目(KJ2012A265 KJ2013A248) 宿州学院博士科研启动基金(2013jb04)
关键词 积分边值问题 分数阶微分方程 Caputo型分数阶导数 不动点定理 integral boundary value problem fractional differential equation Caputo fractional derivative nonlinear alternative principle
分类号 O175.8 [理学—基础数学]
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参考文献10

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同被引文献13

  • 1郭大钧.非线性泛函分析(第二版)[M].济南:山东科技出版社,2004:157-158.
  • 2Podlubny I. Fractional differential equations: an introduction to fractional derivatives, frac- tional differential equations, to methods of their solution and some of their applications[M]. Amsterdam: Elsevier, 1998.
  • 3Kilbas A A, Srivastava H M, Trujillo J J. Theory and Applications of Fractional Differential Equations[M]. Amsterdam: Elsevier, 2006.
  • 4Ahmad B, Nieto J J. Existence results for a coupled system of nonlinear fractional differ- ential equations with three-point boundary conditions[J]. Computers and Mathematics with Applications, 2009, 58(9): 1838-1843.
  • 5Su Xinwei. Boundary value problem for a coupled system of nonlinear fractional differential equations[J]. Applied Mathematics Letters, 2009, 22(1): 64-69.
  • 6Zhao Yige, Sun Shurong, Han Zhenlai, et al. Positive solutions for for a coupled system of nonlinear differential equations of mixed fractional orders[J]. Advance in Difference Equa- tions, 2011: 64-69.
  • 7Yuan Chengjun, Jiang Daqing, O'Regan D, et al. Multiple positive solutions to systems of nonlinear semipositone fractional differential equations with coupled boundary conditions[J]. Electronic Journal Qualitative Theory of Differential Equations, 2012, 2012(13): 1-17.
  • 8Li Yaohong, Wei Zhongli. Positive solutions for a coupled system of mixed higher-order nonlinear singular fractional differential equations[J]. Fixed Point Theory, 2014, 15(1): 167- 178.
  • 9Sudsutad W, Tariboon J. Boundary value problems for fractional differential equations with three-point fractional integral boundary conditions[J]. Advances in Difference Equations, 2012, 2012(1): 1-10.
  • 10Guezane-Lakoud A, KhMdi R . Solvability of a fractional boundary vaule problem with fractional integral condition[J]. Nonlinear Analysis: Theory, Methods and Applications, 2012, 75(4): 2692- 2700.

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高校应用数学学报（A辑）
2014年 第1期

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