JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (03): 73-79.doi: 10.6040/j.issn.1671-9352.0.2014.140

Previous Articles     Next Articles

Existence of positive solutions of the boundary value problem for a class of fractional differential equations with delay

ZHENG Chun-hua1, LIU Wen-bin2   

  1. 1. Basic Department, Shaanxi Polytechnic Institute, Xianyang 712000, Shaanxi, China;
    2. Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China
  • Received:2014-04-08 Revised:2014-09-26 Online:2015-03-20 Published:2015-03-13

PDF (PC)

739

Abstract: A class of fractional differential equation with two-point boundary value problem and delay is studied. By using a fixed point theorem on cones and some analysis technique, some sufficient conditions on the existence of solutions for this boundary value problem are obtained,Some known results are extended and improved.

Key words: delay, two-point boundary value problem, fixed point theorem, cone, fractioal order differential equation

CLC Number: 

  • O175.8
[1] MILLER K S, ROSS B. An introduction to the fractional calculus and fractional differential equations[M]. New York: Wiley, 1993.
[2] PODLUBNY I. Fractional differential equation[M]. San Diego: Academic Press, 1999.
[3] KILBAS A A, SRIVASTAVA H M, TRUJILLO J J. Theory and applications of fractional differential equations[M]. Netherlands: Elsevier B V, 2006.
[4] BAI Zhanbing, LÜ Haishen. Positive solutions of boundary value problems of nonlinear fractional differential equation[J]. J Math Anal Appl, 2005, 311:495-505.
[5] ZHANG Shuqin. Positive solutions for boundary value problems of nonlinear fractional differential equations [J]. Electr J Differential Equations, 2006(36):1-12.
[6] ZHAO Yige, SUN Shurong, HAN Zhenlai. Positive solutions for boundary value problems of nonlinear fractional differential equations[J]. Applied Mathematics and Computation, 2011, 217(16):6950-6958.
[7] ZHANG Yinghan, BAI Zhanbing. Existence of solutions for nonlinear fractional three-point boundary value problems at resonance[J]. J Appl Math Comput, 2011, 36(1/2):417-440.
[8] BAI Zhanbing. Solvability for a class of fractional m-point boundary value problem at resonance[J]. Computers & Mathematics with Applications, 2011,62 (3):1292-1302.
[9] CHEN Taiyong, LIU Wenbin, HU Zhigang. A boundary value problem for fractional differential equation with p-Laplacian operator at resonance[J]. Nonlinear Anal, 2012,75(6):3210-3217.
[10] JIANG Weihua. Eigenvalue interval for multi-point boundary value problems of fractional differential equations[J]. J Appl Math Comput, 2013, 219(9):4570-4575.
[11] LI Xiaoyan, LIU Song, JIANG Wei. Positive solutions for boundary value problem of nonlinear fractional functional differential equations[J]. Applied Mathematics and Computation, 2011, 217(22):9278-9285.
[12] ZHAO Yulin, CHEN Haibo, HUANG Li. Existence of positive solutions for nonlinear fractional functional differential equation[J].Computers & Mathematics with Applications, 2012, 64(10):3456-3467.
[13] 葛渭高. 非线性常微分方程边值问题[M].北京:科学出版社,2007.
[1] CHEN Zijie, ZHAO Dongxia, WANG Yiyan. Stability analysis of recurrent neural network systems with three delays [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(2): 43-49.
[2] ZHANG Fanghong. Existence of weak solutions for a class of non-autonomous second-order delay evolution equations on unbounded domain [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(2): 58-63.
[3] YANG Xiunan, XING Hui. Hopf bifurcation of Brusselator model with cross-diffusion and delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(8): 116-124.
[4] LI Zhiqiang, LU Yanqiong. Existence of positive solution for discrete prescribed mean curvature four-point boundary value problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(5): 40-49.
[5] LUO Yihua, DU Yanfei. Hopf bifurcation in a diffusive generalist predator-prey system with nonlocal competition and time delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(4): 72-83.
[6] XU Yinuo, LIU Libin, YANG Xiu. Adaptive moving grid method for a second-order singularly perturbed delay boundary value problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(12): 84-93.
[7] XI Xia, LI Yongxiang. Periodic solutions of a second-order delay ordinary differential equation with derivative term [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(12): 103-109.
[8] Fangfang HU,Weimin HU,Yong ZHANG. Existence and uniqueness of positive solutions of integral boundary value problems for a class of fractional differential equations with Hadamard derivatives [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 53-61.
[9] LI Cunli. Existence of positive solutions for a class of second-order semi-positone problems with Dirichlet boundary conditions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(12): 96-101.
[10] FAN Jianhang, WU Kuilin. Periodic solutions of a non-autonomous piecewise bilinear system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(12): 114-121.
[11] Yujiao SONG,Qingyuan QI. Optimal local and remote control for multiplicative noise stochastic systems with packet loss and delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 53-63.
[12] Yiyan WANG,Dongxia ZHAO,Caixia GAO. On ramp control of ARZ traffic flow model based on time-delay feedback [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 64-73, 88.
[13] Feng ZHANG,Jiawei LIANG. Sufficient maximum principle for one kind of nonzero-sum stochastic differential game involving noisy memory [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 46-52.
[14] Xiao WANG,Chongyang LIU,Dianzhong HU,Gang LIU. Delay optimal control of 1,3-propanediol batch fermentation [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(1): 124-131, 138.
[15] Yadi WANG,Hailong YUAN. Hopf bifurcation analysis in the Lengyel-Epstein reaction diffusion system with time delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 92-103.
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