一类Caputo分数阶微分方程边值问题的解的存在性
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摘要
研究Banach空间中一类具有Caputo导数的非线性分数阶微分方程边值问题.构建此类方程的格林函数,利用Schauder不动点定理和Banach不动点定理,得到此类方程mild解存在的几个充分条件.
This paper is concerned with the boundary value problem of a class of nonlinear fractional differential equations with Caputo derivative in Banach spaces.By using Green's function, Schauder's fixed point theorem and Banach's fixed point theorem, some sufficient conditions for the existence of the mild solution are obtained.
This paper is concerned with the boundary value problem of a class of nonlinear fractional differential equations with Caputo derivative in Banach spaces.By using Green's function, Schauder's fixed point theorem and Banach's fixed point theorem, some sufficient conditions for the existence of the mild solution are obtained.
引文
[1]Kilbas A A, Srivastava H M, Trujillo J J. Theory and applications of fractional differential equations[M].Amsterdam:Elsevier Science B V, 2006.
[2]蒲亦菲·将分数阶微分演算引入数字图像处理[J].四川大学学报(工程科学版),2007, 39(3):124-132.
[3]周激流.分数阶微积分原理及其在现代信号分析与处理中的应用[M].北京:科学出版社,2010.
[4]张文彪.分数阶微分方程理论及其在生化反应中的应用[D].中国科学院大学,2017.
[5]胡建兵.分数阶混沌稳定性理论及同步方法研究[D].中北大学,2008.
[6]王少伟.分数阶微积分在粘弹性流体力学及量子力学中的某些应用[D].山东大学,2007.
[7]Xu X J, Jiang D Q, Yuan C J. Multiple positive solutions for the boundary value problem of a non-linear fractional differential equation[J]. Nonlinear Analysis, 2009, 71:4676-4688.
[8]杨帅,张淑琴.Caputo型分数阶微分方程边值问题解的存在唯一性[J].郑州大学学报(理学报),2017, 49(2):1-6.
[9]Bai Z, Lii H. Positive solutions for boundary value problem of fractional order[J]. Acta Mathematic Scientia,2006, 26B(2):220-228.
[10]郭彩霞,任玉岗,郭建敏.一类Caputo分数阶微分方程边值问题多解的存在性[J].广西科学,2016, 23(4):374-377.
[11]许晓婕,孙新国,吕炜.非线性分数阶微分方程边值问题正解的存在性[J].数学物理学报,2011,31A(2):401-409.
[12]Ntouyas S K, Tariboon J. Fractional boundary value problems with multiple orders of fractional derivatives and integrals[J]. Electronic Journal of Differential Equations,2017, 2017(100):1-18.
[13]董琪翔,毋光先,李姣. Banach空间中一类分数阶微分方程边值问题[J].纯粹数学与应用数学,2013,29(1):1-10.
[14]Liu X G, Ouyang Z G, Zhong J C. Existence and uniqueness of solutions to a nonlinear fractional differential equation[J]. Ann of Diff Eqs, 2011, 27(1):19-27.
[15]Dai Q, Li H L, Liu S L. Existence and uniqueness of positive solutions for a system of multi-order fractional differential equations[J]. Communications in Mathematical Research, 2016, 32(3):249-258.
[16]陈丽珍,凡震彬,李刚.预解算子控制的无穷时滞分数阶微分方程解的存在性[J].数学杂志,2016, 36(6):1215-1221.
[17]Wu Y Y,Li X Y,Jiang W. Some results for two kinds of fractional equations equations with boundary value problems[J]. J of Math, 2016, 36(5):889-897.
[18]Diethelm K. The analysis of fractional differential equations[M]. Berlin:Springer, 2010.
[19]张恭庆,林源渠.泛函分析讲义(上)[M].北京:北京大学出版社,2005.
[20]李广民,刘三阳.应用泛函分析原理[M].西安:西安电子科技大学出版社,2003:133-134.
[2]蒲亦菲·将分数阶微分演算引入数字图像处理[J].四川大学学报(工程科学版),2007, 39(3):124-132.
[3]周激流.分数阶微积分原理及其在现代信号分析与处理中的应用[M].北京:科学出版社,2010.
[4]张文彪.分数阶微分方程理论及其在生化反应中的应用[D].中国科学院大学,2017.
[5]胡建兵.分数阶混沌稳定性理论及同步方法研究[D].中北大学,2008.
[6]王少伟.分数阶微积分在粘弹性流体力学及量子力学中的某些应用[D].山东大学,2007.
[7]Xu X J, Jiang D Q, Yuan C J. Multiple positive solutions for the boundary value problem of a non-linear fractional differential equation[J]. Nonlinear Analysis, 2009, 71:4676-4688.
[8]杨帅,张淑琴.Caputo型分数阶微分方程边值问题解的存在唯一性[J].郑州大学学报(理学报),2017, 49(2):1-6.
[9]Bai Z, Lii H. Positive solutions for boundary value problem of fractional order[J]. Acta Mathematic Scientia,2006, 26B(2):220-228.
[10]郭彩霞,任玉岗,郭建敏.一类Caputo分数阶微分方程边值问题多解的存在性[J].广西科学,2016, 23(4):374-377.
[11]许晓婕,孙新国,吕炜.非线性分数阶微分方程边值问题正解的存在性[J].数学物理学报,2011,31A(2):401-409.
[12]Ntouyas S K, Tariboon J. Fractional boundary value problems with multiple orders of fractional derivatives and integrals[J]. Electronic Journal of Differential Equations,2017, 2017(100):1-18.
[13]董琪翔,毋光先,李姣. Banach空间中一类分数阶微分方程边值问题[J].纯粹数学与应用数学,2013,29(1):1-10.
[14]Liu X G, Ouyang Z G, Zhong J C. Existence and uniqueness of solutions to a nonlinear fractional differential equation[J]. Ann of Diff Eqs, 2011, 27(1):19-27.
[15]Dai Q, Li H L, Liu S L. Existence and uniqueness of positive solutions for a system of multi-order fractional differential equations[J]. Communications in Mathematical Research, 2016, 32(3):249-258.
[16]陈丽珍,凡震彬,李刚.预解算子控制的无穷时滞分数阶微分方程解的存在性[J].数学杂志,2016, 36(6):1215-1221.
[17]Wu Y Y,Li X Y,Jiang W. Some results for two kinds of fractional equations equations with boundary value problems[J]. J of Math, 2016, 36(5):889-897.
[18]Diethelm K. The analysis of fractional differential equations[M]. Berlin:Springer, 2010.
[19]张恭庆,林源渠.泛函分析讲义(上)[M].北京:北京大学出版社,2005.
[20]李广民,刘三阳.应用泛函分析原理[M].西安:西安电子科技大学出版社,2003:133-134.