JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 66-73.doi: 10.6040/j.issn.1671-9352.0.2015.352
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SU Xiao-feng, JIA Mei*, LI Meng-meng
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| [1] 郑祖庥. 分数微分方程的发展和应用[J]. 徐州师范大学学报:自然科学版,2008, 26(2):1-10. ZHENG Zuxiu. The development and application of fractional differential equation[J]. Journall of Xuzhou Normal University: Natural Science Edition, 2008, 26(2):1-10. [2] ZHANG Xuemei, FENG Meiqiang, GE Weigao. Existence result of second-order differential equations with integral boundary condition at resonance[J]. J Math Anal Appl, 2009, 353(1):311-319. [3] BAI Zhangbing, ZHANG Yinhan. The existence of solutions for a fractional multi-point boundary value problem[J]. Comput Math Appl, 2010, 60(8):2364-2372. [4] 沈立, 刘锡平, 卢振花. 共振条件下三阶三点边值问题解的存在性[J]. 上海理工大学学报, 2010, 32(1):69-72. SHEN Li, LIU Xiping, LU Zhenhua. Existence of solutions for third-order three-point boundary value problems at resonance[J]. Journal of University of Shanghai for Science and Technology, 2010, 32(1):69-72. [5] GUPTA C P. A second order m-point boundary value problem at resonance[J]. Nonlinear Anal, 1995, 24(10):1483-1489. [6] LIU Bing. Solvability of multi-point boundary problem at resonance(II)[J]. Appl Math Comput, 2003, 136(2-3):353-377. [7] LIU Hongliang, OUYANG Zigen. Existence of solutions for second-order three-point integral boundary value problems at resonance[J]. Bound Value Probl, 2013, 2013:197. [8] ZHANG Shuqing, HU Lei, SHI Ailing. Existence result for a nonlinear fractional differential equation with integral boundary conditions at resonance[J]. Adv Difference Equ, 2013, 2013:353. [9] JIANG Weihua. Solvability for fractional differential equations at resonance on the half line[J]. Appl Math Comput, 2014, 247:90-99. [10] BAI Zhanbing, ZHANG Yinghan, Solvability of fractional three-point boundary value problems with nonlinear growth[J]. Appl Math Comput, 2011, 218(5):1719-1725. [11] 白占兵. 分数阶微分方程边值问题理论及应用[M]. 北京: 科学技术出版社, 2012. BAI Zhanbing. Theory and applications of fractional differential equations boundary value problems[M]. Beijing: Science and Technology Press, 2012. [12] 杨浩, 刘锡平, 吴贵云. 一类分数阶p-Laplace 算子微分方程非局部边值问题解的存在性[J]. 山东大学学报(理学版),2014, 50(4):57-62. YANG Hao, LIU Xiping, WU Guiyun. Existence of solutions for a class of nonlocal boundary value problem for fractional differential equations with p-Laplacian[J]. Journal of Shandong University(Natural Science), 2014, 50(4):57-62. [13] 李凡凡, 刘锡平, 智二涛. 分数阶时滞微分方程积分边值问题解的存在性[J]. 山东大学学报(理学版),2013, 48(12):24-29. LI Fanfan, LIU Xiping, ZHI Ertao. Existence of solutions for fractional delay differential equations with integral boundary conditions[J]. Journal of Shandong University(Natural Science), 2013, 48(12):24-29. [14] 刘帅, 贾梅, 秦小娜. 带积分边值条件的分数阶微分方程解的存在性与唯一性[J]. 上海理工大学学报, 2014, 36(5):409-415. LIU Shuai, JIA Mei, QIN Xiaona. Existence and uniqueness of solutions for fractional differential equations with integral boundary conditions[J]. Journal of University of Shanghai for Science and Technology, 2014, 36(5):409-415. [15] PODLUBNY I. Fraction differential equations[M]. New York: Acad Press, 1999. [16] KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equation[M]. Netherlands: Elsevier Science, 2006. [17] 郭大钧, 孙经先, 刘兆理. 非线性常微分方程泛函方法[M]. 2版. 济南: 山东科学技术出版社, 2006. GUO Dajun, SUN Jingxian, LIU Zhaoli. Functional methods for nonlinear ordinary differential equations[M]. 2nd ed. Jinan: Shandong Science and Technology Press, 2006. |
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