留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

一类含参数分数阶微分方程边值问题正解的性质研究

冯海星 翟成波

冯海星, 翟成波. 一类含参数分数阶微分方程边值问题正解的性质研究[J]. 应用数学和力学, 2017, 38(7): 818-826. doi: 10.21656/1000-0887.380124
引用本文: 冯海星, 翟成波. 一类含参数分数阶微分方程边值问题正解的性质研究[J]. 应用数学和力学, 2017, 38(7): 818-826. doi: 10.21656/1000-0887.380124
FENG Hai-xing, ZHAI Cheng-bo. Properties of Positive Solutions to a Class of Fractional Differential Equations With Parameters and Integral Boundary Conditions[J]. Applied Mathematics and Mechanics, 2017, 38(7): 818-826. doi: 10.21656/1000-0887.380124
Citation: FENG Hai-xing, ZHAI Cheng-bo. Properties of Positive Solutions to a Class of Fractional Differential Equations With Parameters and Integral Boundary Conditions[J]. Applied Mathematics and Mechanics, 2017, 38(7): 818-826. doi: 10.21656/1000-0887.380124

一类含参数分数阶微分方程边值问题正解的性质研究

doi: 10.21656/1000-0887.380124
基金项目: 国家自然科学基金(11201272);山西省自然科学基金(2015011005);2015山西省131人才项目
详细信息
    作者简介:

    冯海星(1981—),女,硕士(E-mail: seastar1981@126.com);翟成波(1977—),男,博士(通讯作者. E-mail: cbzhai@sxu.edu.cn).

  • 中图分类号: O177.91

Properties of Positive Solutions to a Class of Fractional Differential Equations With Parameters and Integral Boundary Conditions

Funds: The National Natural Science Foundation of China(11201272)
  • 摘要: 研究了一类含参数的分数阶微分方程边值问题,主要运用锥上的不动点定理及混合单调算子特征值问题的性质得出了正解关于参数的性质:存在唯一性、单调性、连续性以及极限性质.最后举例说明了结果的可行性.
  • [1] Oldham K B, Spanier J. The Fractional Calculus [M]. New York: Academic Press, 1974.
    [2] Samko S G, Kilbas A A , Marichev O I. Fractional Integrals and Derivatives: Theory and Applications [M]. Switzerland: Gordon and Breach Science Publishers, 1993.
    [3] Metzler F, Schick W, Kilian H G, et al. Relaxation in filled polymers: a fractional calculus approach[J]. The Journal of Chemical Physics, 1995,103(16): 7180-7186.
    [4] Goodrich C S. On discrete sequential fractional boundary value problems[J]. Journal of Mathematical Analysis and Applications,2012,385(1): 111-124.
    [5] Lakshmikantham V. Theory of fractional functional differential equations[J]. Nonlinear Analysis: Theory, Methods & Applications,2008,69(10): 3337-3343.
    [6] Kosmatov N. A singular boundary value problem for nonlinear differential equations of fractional order[J]. Journal of Applied Mathematics and Computing,2009,29(1): 125-135.
    [7] BAI Zhan-bing, L Hai-shen. Positive solutions for boundary value problem of nonlinear fractional differential equation[J]. Journal of Mathematical Analysis and Applications,2005,311(2): 495-505.
    [8] LI Ya-ling, LIN Shi-you. Boundary value problem for a coupled system of nonlinear fractional differential equations[J]. Advances in Intelligent Systems and Computing,2013,212: 139-145.
    [9] ZHANG Shu-qing. Positive solutions to singular boundary value problem for nonlinear fractional differential equation[J]. Computers & Mathematics With Applications,2010,59(3): 1300-1309.
    [10] Ferreira R A C. Positive solutions for a class of boundary value problems with fractional q-differences[J]. Computers & Mathematics With Applications,2011,61(2): 367-373.
    [11] YUAN Cheng-jun. Two positive solutions for (n -1, 1)-type semipositone integral boundary value problems for coupled systems of nonlinear fractional differential equations[J]. Communications in Nonlinear Science and Numerical Simulation,2012,17(2): 930-942.
    [12] Mena C J, Harjani J, Sadarangani K. Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems[J]. Boundary Value Problems,2009,2009: 1-10. doi: 10.1155/2009/421310.
    [13] YANG Liu, CHEN Hai-bo. Unique positive solutions for fractional differential equation boundary value problems[J]. Applied Mathematics Letters,2010,23(9): 1095-1098.
    [14] LIANG Si-hua, ZHANG Ji-hui. Existence and uniqueness of strictly nondecreasing and positive solution for a fractional three-point boundary value problem[J]. Computers & Mathematics With Applications,2011,62(3): 1333-1340.
    [15] YANG Chen, ZHAI Cheng-bo. Uniqueness of positive solutions for a fractional differential equation via a fixed point theorem of a sum operator[J]. Electronic Journal of Differential Equations,2012(70): 808-826.
    [16] ZHAI Cheng-bo, YAN Wei-ping, YANG Chen. A sum operator method for the existence and uniqueness of positive solutions to Riemann-Liouville fractional differential equation boundary value problems[J]. Communications in Nonlinear Science and Numerical Simulation,2013,18(4): 858-866.
    [17] YANG Chen. Existence and uniqueness of positive solutions for boundary value problems of a fractional differential equation with a parameter[J]. Hacettepe Journal of Mathematics and Statistics,2015,44(3): 659-667.
    [18] FENG Hai-xing , ZHAI Cheng-bo. Existence and uniqueness of positive solutions for a class of fractional differential equation with integral boundary conditions[J]. Nonlinear Analysis: Modelling and Control,2017,22(2): 160-172.
    [19] El-Shahed M, Al-Askar F M. Positive solutions for boundary value problems of nonlinear fractional q-differential equation[J]. Isrn Mathematical Analysis,2011(11): 5545-5550.
    [20] ZHAO Xiang-kui, CHAI Cheng-wen, GE Wei-gao. Existence and nonexistence results for a class of fractional boundary value problems[J]. Journal of Applied Mathematics and Computing,2013,41(1): 17-31.
    [21] ZHAI Cheng-bo, ZHANG Ling-ling. New fixed point theorems for mixed monotone operators and local existence-uniqueness of positive solutions for nonlinear boundary value problems[J]. Journal of Mathematical Analysis and Applications,2011,382(2): 594-614.
    [22] 郭大钧. 非线性分析中的半序方法[M]. 济南: 山东科学技术出版社, 2000.(GUO Da-jun. A Half Order Method in Nonlinear Analysis [M]. Jinan: Shandong Science and Technology Press, 2000.(in Chinese))
    [23] GUO Da-jun, Lakshmikantham V. Nonlinear Problems in Abstract Cones [M]. Boston: Academic Press Inc, 1988.
  • 加载中
计量
  • 文章访问数:  1224
  • HTML全文浏览量:  202
  • PDF下载量:  544
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-05-05
  • 修回日期:  2017-05-25
  • 刊出日期:  2017-07-15

目录

    /

    返回文章
    返回