一类具有分数阶积分边界条件的分数阶微分方程正解的存在性
蒋自国;董彪;
摘要(Abstract)：
研究了一类具有分数阶积分边界条件的分数阶微分方程的边值问题,利用不动点定理,得到了边值问题正解的存在性和唯一性的充分条件。
关键词(KeyWords)： 正解;分数阶微分方程;积分边界条件;不动点定理
基金项目(Foundation): 四川省科研创新团队(14TD0040);; 阿坝师范学院重点项目(ABA15-19);; 四川省高等教育人才培养质量和教学改革项目(14-156-711)阶段性成果
作者(Author): 蒋自国;董彪;
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DOI:
参考文献(References)：
- [1]Podlubnd I.Fractional differential equations:an introduction to fractional derivatives,fraction differential equations,to methods of their solution and some of their applications[M].Amsterdam:Elsevier,1998.
- [2]Kilbas A A,Srivastava H M,Trujillo J J.Theory and applications of fractional differential equations[M].Amsterdam:Elsevier,2006.
- [3]陈文,孙洪广,李西成等.力学与工程问题的分数阶导数建模[M].北京:科学出版社,2010.
- [4]Bai Z B,H S.Positive solutions for boundary value problem of nonlinear fractional differential equation[J].Journal of Mathematical Analysis and Applications,2005,(2).
- [5]Su Xinwei.Boundary value problem for a coupled system of nonlinear fractional differential equations[J].Applied Mathematics Letters,2009,(1).
- [6]Bai Z B.On positive solutions of a nonlocal fractional boundary value problem[J].Nonlinear Anal,2010,(2).
- [7]Feng M,Liu X,Feng H.The existence of positive solutions to a nonlinear fractional differential equation with integral boundary conditions[J].Advances in Differential Equations,2011,(10).
- [8]Liang S,Zhang J.Existence of positive solutions of m-point boundary value problem for some nonlinear fractional differential equations on an infinite interval[J].Computers&Mathematics with Applications,2011,(11).
- [9]陆心怡,张兴秋,王林.一类分数阶微分方程m点边值问题正解的存在性[J].系统科学与数学,2014,(2).
- [10]高洁,周玮.一类非线性分数阶微分方程边值解的存在性和唯一性[J].应用数学学报,2014,(3).
- [11]郭丽敏,张兴秋.无穷区间上带有积分边值分数阶微分方程的多个正解的存在性[J].系统科学与数学,2014,(6).
- [12]李耀红.一类分数阶微分方程组积分边值问题的正解[J].高校应用数学学报,2015,(1).
- [13]张立新.一类含积分边界条件的分数阶微分方程的正解的存在性[J].应用数学学报,2015,(3).