Initial value problems for arbitrary order fractional differential equations with delay

被引：34
作者：
Yang, Zhihui [1 ,2 ]
Cao, Jinde [2 ]
机构：
[1] Anhui Univ Finance & Econ, Sch Stat & Appl Math, Bengbu 233030, Peoples R China
[2] Southeast Univ, Dept Appl Math, Nanjing 210096, Jiangsu, Peoples R China
来源：
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2013年 / 18卷 / 11期
关键词：
Caputo's fractional derivative; Fractional equation; Delay; Existence and uniqueness; Fixed point theorem; INFINITE DELAY; SYSTEMS; DERIVATIVES; UNIQUENESS; EXISTENCE;
D O I：
10.1016/j.cnsns.2013.03.006
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
By fixed point theory the nonlinear alternative of Leray-Schauder type, and the properties of absolutely continuous functions space, we study the existence and uniqueness of initial value problems for nonlinear higher fractional equations with delay, and obtain some new results involving local and global solutions. (C) 2013 Elsevier B. V. All rights reserved.
引用
收藏
页码：2993 / 3005
页数：13
相关论文
共 36 条
  • [1] On the concept of solution for fractional differential equations with uncertainty
    Agarwal, Ravi P.
    Lakshmikantham, V.
    Nieto, Juan J.
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (06) : 2859 - 2862
  • [2] Necessary and sufficient stability condition of fractional-order interval linear systems
    Ahn, Hyo-Sung
    Chen, YangQuan
    [J]. AUTOMATICA, 2008, 44 (11) : 2985 - 2988
  • [3] [Anonymous], 2006, THEORY APPL FRACTION, DOI DOI 10.1016/S0304-0208(06)80001-0
  • [4] [Anonymous], 1993, INTRO FRACTIONAL CA
  • [5] [Anonymous], 1999, FRACTIONAL DIFFERENT
  • [6] Fractional order differential equations on an unbounded domain
    Arara, A.
    Benchohra, M.
    Hamidi, N.
    Nieto, J. J.
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (02) : 580 - 586
  • [7] The nonlocal Cauchy problem for nonlinear fractional integrodifferential equations in Banach spaces
    Balachandran, Krishnan
    Trujillo, Juan J.
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (12) : 4587 - 4593
  • [8] Existence results for fractional order functional differential equations with infinite delay
    Benchohra, A.
    Henderson, J.
    Ntouyas, S. K.
    Ouahab, A.
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 338 (02) : 1340 - 1350
  • [9] Boundary value problems for differential equations with fractional order and nonlocal conditions
    Benchohra, M.
    Hamani, S.
    Ntouyas, S. K.
    [J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (7-8) : 2391 - 2396
  • [10] Control of a fractional-order economical system via sliding mode
    Dadras, Sara
    Momeni, Hamid Reza
    [J]. PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2010, 389 (12) : 2434 - 2442
1234