On the solutions for impulsive fractional functional differential equations

被引：24
作者：
Chen F. [1 ]
Chen A. [2 ]
Wang X. [1 ]
机构：
[1] Department of Mathematics, Xiangnan University
[2] Department of Mathematics, School of Mathematics and Computational Science, Xiangtan University
来源：
Differential Equations and Dynamical Systems | 2009年 / 17卷 / 4期
基金：
中国国家自然科学基金;
关键词：
Existence; Fractional functional differential equation; Impulse; Uniform stability; Uniqueness;
D O I：
10.1007/s12591-009-0027-5
中图分类号：
学科分类号：
摘要：
In this paper, the existence, uniqueness and uniform stability of solutions for a class of impulsive fractional functional differential equations are investigated by applying new boundedness condition and Lipschitz condition. An example is given to illustrate the main results. © 2009 Foundation for Scientific Research and Technological Innovation.
引用
收藏
页码：379 / 391
页数：12
相关论文
共 16 条
  • [1] Podlubny I., Fractional Differential Equations, (1999)
  • [2] Zhou Y., Existence and uniqueness of solutions for a system of fractional differential equations, Fractional Calculus and Applied Analysis, 12, pp. 195-204, (2009)
  • [3] Delbosco D., Rodino L., Existence and uniqueness for a nonlinear fractional differential equation, J. Math. Anal. Appl, 204, pp. 609-625, (1996)
  • [4] Zhang S., The existence of a positive solution for a nonlinear fractional differential equation, J. Math. Anal. Appl, 252, pp. 804-812, (2000)
  • [5] Diethelm K., Ford N.J., Analysis of fractional differential equations, J. Math. Anal. Appl, 265, pp. 229-248, (2002)
  • [6] Daftardar-Gejji V., Positive solutions of a system of non-autonomous fractional differential equations, J. Math. Anal. Appl, 302, pp. 56-64, (2005)
  • [7] Yu C., Gao G., Existence of fractional differential equations, J. Math. Anal. Appl, 310, pp. 26-29, (2005)
  • [8] El-Sayed A.M.A., Nonlinear functional differential equations of arbitrary orders, Nonlinear Anal, 33, pp. 181-186, (1998)
  • [9] Lakshmikantham V., Theory of fractional functional differential equations, Nonlinear Anal, 69, pp. 3337-3343, (2008)
  • [10] Benchohra M., Henderson J., Ntouyas S.K., Ouahab A., Existence results for fractional order funtional differential equations with infinite delay, J. Math. Anal. Appl, 338, pp. 1340-1350, (2008)
12