[1]薛益民,戴振祥.一类非线性Riemann-Liouville分数阶 微分方程耦合系统的正解[J].徐州工程学院学报(自然科学版),2019,(03):64-68.
 XUE Yimin,DAI Zhenxiang.Positive Solutions to a Coupled System of Nonlinear Riemann-Liouville Fractional Differential Equations[J].Journal of Xuzhou Institute of Technology(Natural Sciences Edition),2019,(03):64-68.
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一类非线性Riemann-Liouville分数阶 微分方程耦合系统的正解()
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《徐州工程学院学报》(自然科学版)[ISSN:1674-358X/CN:32-1789/N]

卷:
期数:
2019年03期
页码:
64-68
栏目:
应用基础研究
出版日期:
2019-09-15

文章信息/Info

Title:
Positive Solutions to a Coupled System of Nonlinear Riemann-Liouville Fractional Differential Equations
文章编号:
1674-358X(2019)03-0064-05
作者:
薛益民戴振祥
(徐州工程学院 数学与物理科学学院,江苏 徐州221018)
Author(s):
XUE YiminDAI Zhenxiang
(School of Mathematics and Physics,Xuzhou University of Technology,Xuzhou 221018,China)
关键词:
分数阶微分方程 Green函数 耦合系统 正解
Keywords:
fractional differential equations Green's function coupled system positive solution
分类号:
O175.8
文献标志码:
A
摘要:
文章研究一类非线性Riemann-Liouville型分数阶微分方程耦合系统正解的存在性和唯 一性.借助格林函数的性质,运用Leray-Schauder抉择理论和Banach压缩映射原理,得到了该 耦合系统正解的存在性和唯一性的充分条件,并举例说明了定理的有效性.
Abstract:
In this paper,the existence and uniqueness of positive solutions for a class of coupled systems of nonlinear Riemann-Liouville fractional differential equations are studied.The existence and uniqueness of positive solutions were obtained by using the properties of the associated Green's function and the nonlinear alternative of Leray-Schauder type and Banach contraction mapping principle.The validity of the theorem is illustrated by examples.

参考文献/References:

[1] SUN Y,ZHAO M.Positive solutions for a class of fractional differential equations with integral boundary conditions[J].Applied Mathematics Letters,2014,34:17-21.
[2] ZHANG X,WANG L,SUN Q.Existence of positive solutions for a class of nonlinear Fractional Differential Equations with Integral Boundary Conditions and a Parameter[J].Applied Mathematics and Computation,2014,226:708-718.
[3] SHAH K,KHAN R A.Existence and uniqueness of positive solutions to a coupled system of nonlinear fractional order differential equations with anti- periodic boundary conditions[J].Differential Equations & Application,2015,7 (2):245-262.
[4] AHMAD B,NTOUYAS S K.A fully hadamard type integral boundary value problem of a coupled system of fractional differential equations[J].Fractional Calculus and Applied Analysis,2014,17(2):348-360.
[5] SHAH K,KHALIL H,KHAN R A.Upper and lower solutions to a coupled system of nonlinear fractional differential equations[J].Progress in Fractional Differentiation and Application,2016,2(1):1-10.
[6] WANG Y,LIU L,WU Y.Positive solutions for a class of fractional boundary value problem with changing sign nonlinearity[J].Nonlinear Analysis,2011,74 (17):6434-6441.
[7] KILBAS A A,SRIVASTAVA H M,TRUJILLO J J.Theory and applications of fractional differential equations[M].Amsterdam:Elsevier,2006.
[8] PODIUBNY I.Fractional differential equations[M].San Diego:Academic Press,1999.
[9] GRANAS A,DUGUNDJI J.Fixed point theory[M].New York:Springer,2005.[ZK)]
[10] DEIMLING K.Nonlinear functional analysis[M].Berlin:Springer,1985.
[11]薛益民,苏有慧,刘洁,等.一类分数阶微分方程耦合系统边值问题解的存在性[J], 徐州工程学院学报(自然科学版),2018,33(1):41-47.

相似文献/References:

[1]吴彦强.一类分数阶微分方程共振边值问题解的存在性[J].徐州工程学院学报(自然科学版),2016,(2):40.
 WU Yanqiang.Solvability for a Class of Fractional m-Point Boundary Value Problem at Resonance[J].Journal of Xuzhou Institute of Technology(Natural Sciences Edition),2016,(03):40.
[2]薛益民,苏有慧,刘洁,等.一类分数阶微分方程耦合系统边值问题解的存在性[J].徐州工程学院学报(自然科学版),2018,(1):41.
 XUE Yimin,SU Youhui,LIU Jie,et al.Existence of Solutions of the Boundary Value Problem to a Coupled System of a Certain Fractional Differential Equation[J].Journal of Xuzhou Institute of Technology(Natural Sciences Edition),2018,(03):41.

备注/Memo

备注/Memo:
收稿日期:2018-05-27 基金项目:[ZK(]国家自然科学数学天元基金项目(11526177); 江苏省自然科学基金项目 (BK20151160); 徐州工程学院培育项目(XKY2017113)[ZK)] 作者简介:薛益民(1977-),男,副教授,博士研究生,主要从事微分方程理论及应用研究.
更新日期/Last Update: 2019-09-15