山东大学学报(理学版) ›› 2015, Vol. 50 ›› Issue (04): 42-48.doi: 10.6040/j.issn.1671-9352.0.2014.157
陈强, 贾梅, 张海斌
CHEN Qiang, JIA Mei, ZHANG Hai-bin
摘要: 研究了一类非线性分数阶微分方程四点边值问题解的存在性和唯一性,利用Schauder不动点定理以及压缩映像原理,得到了边值问题解的存在性以及唯一性的充分条件.
中图分类号:
[1] 白占兵. 分数阶微分方程边值问题理论及应用[M]. 北京: 中国科学技术出版社, 2012. [2] PODLUBNY I. Fraction differential equations[M]. New York: Acad Press, 1999. [3] DIETHELM K. The analysis of fractional differential equations[M]. Heidelberg: Spring-Verlag, 2010. [4] KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. North-Holland Mathematics Studies, Vol.204, Elsevier Science B V Amsterdam, 2006. [5] SU Xinwei, LIU Landong. Existence of solution for boundary value problem of nonlinear fractional differential equation[J]. Applied Mathematics A Journal of Chinese Universities: B, 2007, 22(3):291-298. [6] BAI Zhanbing, SUN Weichen. Existence and multiplicity of positive solutions for singular fractional boundary value problems[J]. Computers and Mathematics with Applications, 2012, 63(9):1369-1381. [7] SVATOSLAV S. The existence of positive solutions of singular fractional boundary value problems[J]. Computers and Mathematics with Applications, 2011, 62(3):1379-1388. [8] ZHAO Xiangkui, CHAI Chengwen, GE Weigao. Positive solutions for fractional four-point boundary value problems[J]. Commun Nonlinear Sci Numer Simulat, 2011, 16(9):3665-3672. [9] FENG Meiqiang, ZHANG Xuemei, GE Weigao. New existence results for higher-order nonlinear fractional differential equation with integral boundary conditions[J]. Boundary Value Problems, 2011, 2011:1-20. [10] 方海琴, 刘锡平, 林乐刚.分数阶微分方程反周期边值问题解的存在性[J]. 山东大学学报:理学版, 2012, 47(6):5-9. FANG Haiqin, LIU Xiping, LIN Legang. Existence of a solution for anti-periodic boundary value problems of fractional differential equations[J]. Journal of Shandong University: Natural Science, 2012, 47(6):5-9. [11] 窦丽霞, 刘锡平, 金京福,等. 分数阶积分微分方程多点边值问题解的存在性和唯一性[J]. 上海理工大学学报, 2012, 34(1):52-55. DOU Lixia, LIU Xiping, JIN Jingfu, et al. Existence and uniqueness of solutions of multi-point boundary value problems for integro-differential equations of fractional order[J]. Journal of University of Shanghai for Science and Technology, 2012, 34(1):52-55. [12] NYAMORADI N. Existence of solutions for multi-point boundary value problem for fractional differential equations[J]. Arab Journal of Mathematical Sciences, 2012, 18:165-175. [13] 王淑, 贾梅, 祁卫杰. 非线性项变号的分数阶微分方程边值问题正解的存在性[J]. 上海理工大学学报, 2013, 35(1):1-6. WANG Shu, JIA Mei, QI Weijie, Existence of positive solutions for a class of fractional differential equations with sign changing nonlinearities[J]. Journal of University of Shanghai for Science and Technology, 2013, 35(1):1-6. [14] SALEM H A H. On the fractional order m-point boundary value problem in reflexive Banach spaces and weak topologies[J]. Journal of Computational and Applied Mathematics, 2009, 224(2):565-572. [15] 秦小娜, 贾梅, 刘帅. 具Caputo导数分数阶微分方程边值问题正解的存在性[J]. 山东大学学报:理学版, 2013, 48(10):62-67. QIN Xiaona, JIA Mei, LIU Shuai, Existence of positive solutions for fractional differential equations boundary value problems with Caputo derivative[J]. Journal of Shandong University: Natural Science, 2013, 48(10):62-67. [16] BAI Zhanbing, LU Haishen. Positive solution for boundary value problem of nonlinear fractional differential equation[J]. Journal of Mathematical Analysis and Application, 2005, 311(2):495-505. |
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