JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (8): 66-73.doi: 10.6040/j.issn.1671-9352.0.2015.352

Previous Articles     Next Articles

Existence of solution for fractional differential equation integral boundary value problem at resonance

SU Xiao-feng, JIA Mei*, LI Meng-meng   

  1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
  • Received:2015-07-27 Online:2016-08-20 Published:2016-08-08

PDF (PC)

1149

Abstract: Existence of solutions for a class of fractional differential equations with integral boundary conditions is studied at resonance. By using coincidence degree theory, we obtain and prove the theorem about existence of solutions for the integral boundary value problem with dim Ker L=2.

Key words: fractional differential equation, integral boundary value problem, resonance, coincidence degree theory, Caputo derivative

CLC Number: 

  • O175.8
[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.
[1] YE Fu-mei. Existence results of a resonance problem with derivative terms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 25-31.
[2] 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.
[3] ZHANG Di, LIU Wen-bin. Existence of solutions for p(t)-Laplacian fractional infinite-point boundary value problems at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 72-80.
[4] ZHONG Qiu-yan, ZHANG Xing-qiu. Positive solutions for some singular fractional differential equation integral boundary value problems with p-Laplacian and a parameter [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 78-84.
[5] SU Yan. Existence of solutions for second-order discrete Neumann problems at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 37-41.
[6] CHEN Bin, Abuelgasimalshaby Elzebir. Existence and multiplicity results for a second-order multi-point boundary value problem at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 49-52.
[7] 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.
[8] CHEN Yi-ming, KE Xiao-hong, HAN Xiao-ning, SUN Yan-nan, LIU Li-qing. Wavelets method for solving system of fractional differential equations and the convergence analysis [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 67-74.
[9] 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.
[10] HEN Yi-ming, SUN Hui, LIU Le-chun, FU Xiao-hong. Legendre polynomial method for solving Fredholm integro-differential  equations of fractional order with variable coefficient [J]. J4, 2013, 48(6): 80-86.
[11] LI Fan-fan, LIU Xi-ping*, ZHI Er-tao. Existence of a solution for the boundary value problem of
fractional differential equation with delay [J]. J4, 2013, 48(12): 24-29.
[12] QIN Xiao-na, JIA Mei*, LIU Shuai. Existence of positive solutions for fractional differential equations boundary value problems with Caputo derivative [J]. J4, 2013, 48(10): 62-67.
[13] LI Ming, XU Ming-yu. Solving the fractional order Bloch equation [J]. J4, 2013, 48(1): 56-61.
[14] WEI Wang-he, HOU Chun-ju, LU Min, LIU Wei-qing. Theoretical explanation of the anisotropic g factors for Cu2+ center in Cu0.5Zr2(PO4)3crystal [J]. J4, 2012, 47(7): 26-29.
[15] FANG Hai-qin, LIU Xi-ping*, LIN Le-gang. Existence of a solution for anti-periodic boundary value problems of  fractional differential equations [J]. J4, 2012, 47(6): 5-9.
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