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非线性分数阶微分积分方程多点分数阶边值问题解的存在性与唯一性(英文) 被引量：4

Existence and Uniqueness of Solutions for Multi-point Fractional Boundary Value Problems for Nonlinear Fractional Integro-differential Equations
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摘要 本文研究一类非线性分数阶微分积分方程多点分数阶边值问题解的存在性与唯一性,利用一些标准的不动点定理进行证明. In this paper, we investigate the existence and uniqueness of solutions for a class of multi-point fractional boundary value problems for nonlinear fractional integro-differential equations. Our analysis relies on the some standard fixed point theorems.
作者 马俊驰 杨军
机构地区 燕山大学理学院 河北省数学研究中心
出处 《应用数学》 CSCD 北大核心 2011年第3期575-580,共6页 Mathematica Applicata
基金 Supported by the NNSF of China(60604004) the Special Projects in Mathematics Funded by NSF of Hebei Province(07M005) the Science and Technology Support Project of Qinhuangdao(201001A037)
关键词 非线性分数阶微分方程 多点分数阶边值问题 不动点定理 Nonlinear fractional differential equation Multi-point fractional boundary value problem Fixed point theorem
分类号 O175.8 [理学—基础数学]
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参考文献6

  • 1Podlubny I. Fractional Differential Equations[M]. New York: Mathematics in Science and Engineering Academic Press, 1999.
  • 2Mujeeb ur Rehman,Rahmat Ali Khan. Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations[J]. AppI. Math. Lett. , 2010,23:1038-1044.
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同被引文献24

  • 1刘式达,时少英,刘式适,梁福明.天气和气候之间的桥梁——分数阶导数[J].气象科技,2007,35(1):15-19. 被引量：15
  • 2杨军,马俊驰,赵硕,等.分数阶微分方程多点分数阶边值问题[J].数学实践与认识,2011,41(11):188-194.
  • 3HILFER R. Applications of fractional calculus in physics [ M ]. Singapore : World Scientific, 2000.
  • 4LAKSHMIKANTHAM V, LEELA S, VASUNDHARA DEVI J. Theory of fractional dynamic systems [ M ]. Cambridge: Cambridge Academic Publishers, 2009.
  • 5BALACHANDRAN K, KIRUTHIKA S, TRUJILLO J J. Existence results for fractional impulsive integro differenti- al equations in Banach spaces [ J ]. Commun Nonlinear Sci Numer Simulat, 2011, 16 (4) : 1970 - 1977.
  • 6WANG G T, AHMAD B, ZHANG L H. Impulsive anti- periodic boundary value problem for nonlinear differential equations of fractional order [ J]. Nonlinear Anal, 2011, 74(3) :792 -804.
  • 7WANG X H. Impulsive boundary value problem for non- linear differential equations of fractional order [ J ]. Com- puters and Mathematics with Application, 2011,62(5 ) : 2383 - 2391.
  • 8WANG J R, ZHOU Y, FECKAN M. Nonlinear impulsive problems for fractional differential equation and Ulam sta- bility [J]. Computers and Mathematics with Application, 2012, 64(10): 3008-3020.
  • 9MA J C, YANG J. Existence of solutions for multi-point boundary value problem of fractional q-differential equa- tion [ J]. Electronic Journal of Qualitative Theory of Dif- ferential Equations, 2011, 92:1 -10.
  • 10MA J C, YANG J. Positive solutions of the multiple point boundary value problems for nonlinear fractional differential equations [ C]//The 2nd International Con- ference on Multimedia Technology, Hangzhou, 2011 : 2293 - 2296.

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应用数学
2011年 第3期

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