JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (04): 42-48.doi: 10.6040/j.issn.1671-9352.0.2014.157

Previous Articles     Next Articles

Existence and uniqueness of solutions for nonlinear fractional four-point boundary value problems

CHEN Qiang, JIA Mei, ZHANG Hai-bin   

  1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2014-04-14 Revised:2014-09-26 Online:2015-04-20 Published:2015-04-17

PDF (PC)

707

Abstract: This paper investigates existence and uniqueness of solutions for a type of four-point boundary value problems with fractional order differential equation.By using the Schauder fixed point theorem and the Banach contraction principle,we obtain the sufficient conditions of the existence and uniqueness of solutions for the nonlinear fractional four-point boundary value problems.

Key words: fixed point theorem, existence and uniqueness, four-point boundary value problems, fractional order differential equation

CLC Number: 

  • O175.8
[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.
[1] SHEN Liu-xiao, ZHAO Chun. Optimal control for inputting rate of a size-structure competitive system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 21-29.
[2] CAO Xue-jing, LUO Zhi-xue. Optimal control of forest evolution system in polluted environment [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(7): 15-20.
[3] WANG Su-yun, LI Yong-jun. Solvability of nonlinear second-order boundary value problems with nonlinearities which cross the resonance points [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 53-56.
[4] XIAO Xin-ling. Forward-backward stochastic differential equations on Markov chains [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 46-54.
[5] LI Tao-tao. Existence of radial positive solutions of second-order semi-positone elliptic differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(4): 48-55.
[6] ZHANG Sha, JIA Mei, LI Yan, LI Xiao-chen. Existence and uniqueness of solutions for three point boundary value problems of impulsive fractional differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 66-72.
[7] FENG Hai-xing, ZHAI Cheng-bo. Multiple positive solutions of a system of high order nonlinear fractional differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 48-57.
[8] RONG Wen-ping, CUI Jing. μ-pseudo almost automorphic solutions for a class of stochastic evolution equations under non-Lipschitz conditions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 64-71.
[9] CHEN Bin. Third-order periodic boundary value problems with sign-changing Greens function [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 79-83.
[10] WU Cheng-ming. Existence of positive periodic solutions for second order singular coupled systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 81-88.
[11] WANG Xian-fei, JIANG Long, MA Jiao-jiao. Multidimensional backward doubly stochastic differential equations with generators of Osgood type [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(08): 24-33.
[12] YANG Hao, LIU Xi-ping, WU Gui-yun. Existence of the solutions for a type of nonlocal boundary value problems for fractional differential equations with p-Laplacian operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(04): 56-62.
[13] ZHENG Chun-hua, LIU Wen-bin. Existence of positive solutions of the boundary value problem for a class of fractional differential equations with delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(03): 73-79.
[14] YANG Xue-jie, SUN Guo-zheng*, CHEN Wen. Shock solution for a quasilinear singularly perturbed problem#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 79-83.
[15] ZHOU Wen-xue1,2, LIU Hai-zhong1. Existence of solution for the  boundary value problem of a class of fractional differential equation [J]. J4, 2013, 48(8): 45-49.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd