数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (5): 1295-1318.doi: 10.1016/S0252-9602(17)30074-7

• 论文 • 上一篇    下一篇

GLOBALLY ATTRACTING SOLUTIONS TO IMPULSIVE FRACTIONAL DIFFERENTIAL INCLUSIONS OF SOBOLEV TYPE

Van Hien LE1, Dinh Ke TRAN1, Trong Kinh CHU2   

  1. 1. Department of Mathematics, Hanoi National University of Education 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam;
    2. Department of Mathematics, Hanoi Pedagogical University No. 2, Vinhphuc, Vietnam
  • 收稿日期:2016-04-12 修回日期:2016-09-22 出版日期:2017-10-25 发布日期:2017-10-25
  • 通讯作者: Dinh Ke TRAN,E-mail:ketd@hnue.edu.vn E-mail:ketd@hnue.edu.vn
  • 作者简介:Van Hien LE,E-mail:hienlv@hnue.edu.vn;Trong Kinh CHU,E-mail:chutrongkinh@gmail.com
  • 基金资助:

    This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2015.18.

GLOBALLY ATTRACTING SOLUTIONS TO IMPULSIVE FRACTIONAL DIFFERENTIAL INCLUSIONS OF SOBOLEV TYPE

Van Hien LE1, Dinh Ke TRAN1, Trong Kinh CHU2   

  1. 1. Department of Mathematics, Hanoi National University of Education 136 Xuan Thuy, Cau Giay, Hanoi, Vietnam;
    2. Department of Mathematics, Hanoi Pedagogical University No. 2, Vinhphuc, Vietnam
  • Received:2016-04-12 Revised:2016-09-22 Online:2017-10-25 Published:2017-10-25
  • Contact: Dinh Ke TRAN,E-mail:ketd@hnue.edu.vn E-mail:ketd@hnue.edu.vn
  • Supported by:

    This research was supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2015.18.

摘要:

We study a generalized Cauchy problem associated with a class of impulsive fractional differential inclusions of Sobolev type in Banach spaces. Our aim is to prove the existence of a compact set of globally attracting solutions to the problem in question. An application to fractional partial differential equations subject to impulsive effects is given to illustrate our results.

关键词: globally attracting solution, impulsive condition, nonlocal condition, condensing map, measure of non-compactness, MNC-estimate

Abstract:

We study a generalized Cauchy problem associated with a class of impulsive fractional differential inclusions of Sobolev type in Banach spaces. Our aim is to prove the existence of a compact set of globally attracting solutions to the problem in question. An application to fractional partial differential equations subject to impulsive effects is given to illustrate our results.

Key words: globally attracting solution, impulsive condition, nonlocal condition, condensing map, measure of non-compactness, MNC-estimate