• Overview of Chinese core journals
  • Chinese Science Citation Database(CSCD)
  • Chinese Scientific and Technological Paper and Citation Database (CSTPCD)
  • China National Knowledge Infrastructure(CNKI)
  • Chinese Science Abstracts Database(CSAD)
  • JST China
  • SCOPUS
XUE Yimin, PENG Zhongqi. On the Existence of Positive Solutions to the Coupled System of a Class of Nonlinear Fractional Differential Equations[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(2): 102-106. DOI: 10.6054/j.jscnun.2020032
Citation: XUE Yimin, PENG Zhongqi. On the Existence of Positive Solutions to the Coupled System of a Class of Nonlinear Fractional Differential Equations[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(2): 102-106. DOI: 10.6054/j.jscnun.2020032

On the Existence of Positive Solutions to the Coupled System of a Class of Nonlinear Fractional Differential Equations

More Information
  • Received Date: July 08, 2019
  • Available Online: March 21, 2021
  • The Guo-Krasnoselskii's fixed point theorem, the Schauder fixed point theorem and the properties of the associated Green's function are used to study the existence of positive solutions to the coupled system of a class of nonlinear Riemann-Liouville fractional differential equations. Two theorems about the existence of positive solutions are obtained, and two examples are given to illustrate the advantages of the theorems.
  • [1]
    SUN Y P, ZHAO M. Positive solutions for a class of fractional differential equations with integral boundary conditions[J]. Applied Mathematics Letters, 2014, 34:17-21. doi: 10.1016/j.aml.2014.03.008
    [2]
    ZHANG X Q, 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. doi: 10.1016/j.amc.2013.10.089
    [3]
    CHEN T Y, LIU W B, HU Z G. A boundary value pro-blem for fractional differential equation with P-Laplacian operator at resonance[J]. Nonlinear Analysis, 2012, 75(6):3210-3217. doi: 10.1016/j.na.2011.12.020
    [4]
    GOODRICH C S. On a fractional boundary value problem with fractional boundary conditions[J]. Applied Mathematics Letters, 2012, 25(8):1101-1105. doi: 10.1016/j.aml.2011.11.028
    [5]
    GRAEF J R, KONG L J. Positive solutions for a class of higher order boundary value problems with fractional Q-derivatives[J]. Applied Mathematics and Computation, 2012, 218(19):9682-9689. doi: 10.1016/j.amc.2012.03.006
    [6]
    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 & Applications, 2015, 7(2):245-262.
    [7]
    JIANG W H. Solvability for a coupled system of fractional differential equations with integral boundary conditions at resonance[J]. Advances in Differential Equations, 2013, 324:1-13. doi: 10.1186/1687-1847-2013-324
    [8]
    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. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=47f19bd98d1cc43baee8c8424dcbe7a8
    [9]
    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 Applications, 2016, 2(1):1-10. doi: 10.18576/pfda/020101
    [10]
    BAI Z B, LU H S. Positive solutions for boundary value problem of nonlinear fractional differential equation[J]. Journal of Mathematical Analysis and Applications, 2005, 311:495-505. doi: 10.1016/j.jmaa.2005.02.052
    [11]
    KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. Amsterdam:Elsevier, 2006.
    [12]
    GUO D J, LAKSHMIKANTHAM V. Nonlinear problems in abstract cones[M]. San Diego:Academic Press, 1988.
    [13]
    GRANAS A, DUGUNDJI J. Fixed point theory[M]. New York:Springer, 2005.
    [14]
    薛益民, 戴振祥, 刘洁.一类Riemann-Liouville型分数阶微分方程正解的存在性[J].华南师范大学学报(自然科学版), 2019, 51(2):105-109. doi: 10.6054/j.jscnun.2019033

    XUE Y M, DAI Z X, LIU J. On the existence of positive solutions to a type of Riemann-Liouville fractional diffe-rential equations[J]. Journal of South China Normal University(Natural Science Edition), 2019, 51(2):105-109. doi: 10.6054/j.jscnun.2019033
    [15]
    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.

    XUE Y M, SU Y H, LIU J, et al. Existence of solutions of the boundary value problem to a coupled system of a certain fractional differential equations[J]. Journal of Xuzhou Institute of Technology(Natural Science Edition), 2018, 33(1):41-47.
  • Cited by

    Periodical cited type(1)

    1. 邱晨,潘凯玲,魏钰轩,郑志强,韩家乐,毕学军. 中低温条件下城市污水短程硝化控制方法研究. 环境科学与技术. 2024(11): 170-177 .

    Other cited types(3)

Catalog

    Article views (1695) PDF downloads (54) Cited by(4)

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return