一类有序分数阶微分方程积分边值问题解的存在性
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摘要
利用Banach压缩映射原理和Krasnoselskill不动点定理,考虑一类具有Riemann-Liouville分数阶积分条件的Caputo型有序分数阶微分方程边值问题,得到了该问题存在唯一解和至少一个解的充分条件,并举例说明结果的应用.
By using Banach's contraction mapping principle and Krasnoselskill's fixed point theorem,we considered a class of boundary value problems of Caputo type sequential fractional differential equations with Riemann-Liouville fractional integral conditions,obtained sufficient conditions for the existence of unique solution and at least one solution to the problem,and gave an example to illustrate the application of the result.
By using Banach's contraction mapping principle and Krasnoselskill's fixed point theorem,we considered a class of boundary value problems of Caputo type sequential fractional differential equations with Riemann-Liouville fractional integral conditions,obtained sufficient conditions for the existence of unique solution and at least one solution to the problem,and gave an example to illustrate the application of the result.
引文
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[6]张海燕,李耀红.一类Hadamard分数阶微分方程边值问题解的存在唯一性[J].四川大学学报(自然科学版),2018,55(4):683-687.(ZHANG Haiyan,LI Yaohong.Existence and Uniqueness of Solution for Boundary Value Problems for a Class of Hadamard Fractional Differential Equations[J].Journal of Sichuan University(Natural Science Edition),2018,55(4):683-687.)
[7]AHMAD B,NIETO J J.Boundary Value Problems for a Class of Sequential Integrodifferential Equations of Fractional Order[J/OL].J Func Spaces Appl,2013-03-13.http://dx.doi.org/10.1155/2013/149659.
[8]AHMAD B,NTOUYAS S K.Existence Results of Caputo Type Sequential Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions[J].J Appl Math Comput,2016,50(1/2):157-174.
[9]JIANG Jiqiang,LIU Lishan.Existence of Solutions for a Sequential Fractional Differential System with Coupled Boundary Conditions[J].Bound Value Probl,2016-08-30.https://doi.org/10.1186/s13661-016-0666-8.
[10]DEIMLING K.Ordinary Differential Equations in Banach Spaces[M].Berlin:Springer,1977.
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[2]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.(CHEN Wen,SUN Hongguang,LI Xicheng,et al.The Fractional Order Derivative Modeling to Mechanics and Engineering Problems[M].Beijing:Science Press,2010.)
[3]ANASTASIO T J.The Fractional-Order Dynamics of Brainstem Vestibulo-Oculomotor Neurons[J].Biol Cybern,1994,72(1):69-79.
[4]AHMAD B,NIETO J J.Sequential Fractional Differential Equations with Three-Point Boundary Conditions[J].Comput Math Appl,2012,64(10):3046-3052.
[5]范成涛,林爽,葛琦.一类新的有序分数阶q-差分系统边值问题解的存在性[J].吉林大学学报(理学版),2018,56(2):219-226.(FAN Chengtao,LIN Shuang,GE Qi.Existence of Solutions for Boundary Value Problems with a New Class of Sequential Fractional q-Differences System[J].Journal of Jilin University(Science Edition),2018,56(2):219-226.)
[6]张海燕,李耀红.一类Hadamard分数阶微分方程边值问题解的存在唯一性[J].四川大学学报(自然科学版),2018,55(4):683-687.(ZHANG Haiyan,LI Yaohong.Existence and Uniqueness of Solution for Boundary Value Problems for a Class of Hadamard Fractional Differential Equations[J].Journal of Sichuan University(Natural Science Edition),2018,55(4):683-687.)
[7]AHMAD B,NIETO J J.Boundary Value Problems for a Class of Sequential Integrodifferential Equations of Fractional Order[J/OL].J Func Spaces Appl,2013-03-13.http://dx.doi.org/10.1155/2013/149659.
[8]AHMAD B,NTOUYAS S K.Existence Results of Caputo Type Sequential Fractional Differential Inclusions with Nonlocal Integral Boundary Conditions[J].J Appl Math Comput,2016,50(1/2):157-174.
[9]JIANG Jiqiang,LIU Lishan.Existence of Solutions for a Sequential Fractional Differential System with Coupled Boundary Conditions[J].Bound Value Probl,2016-08-30.https://doi.org/10.1186/s13661-016-0666-8.
[10]DEIMLING K.Ordinary Differential Equations in Banach Spaces[M].Berlin:Springer,1977.
[11]GUO Dajun,LAKSKMIKANTHAM V.Nonlinear Problems in Abstract Cones[M].New York:Academic Press,1988.