Description

• Title:
  Local and nonlocal problems for fractional impulsive evolution systems with order $\nu\in(1,2)$
• Creator:
  Qiu, Kee;
  Fečkan, Michal;
  Wang, JinRong
• Description:
  In this paper, we study the existence and uniqueness of $PC$-mild solutions for fractional impulsive evolution systems with Caputo derivative. First, we give a compact result of the solution operators of linear fractional evolution system while the cosine family is compact. Second, the representation of $PC$-mild solutions of linear fractional impulsive systems with initial value conditions and nonlocal initial value conditions are given by using the Laplace transform method. Third, several sufficient conditions for judging the existence and uniqueness of solutions of our problem are established via some fixed point theorems and operator semigroup theory. Finally, an example is given to illustrate the results of our paper.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2024 Kee Qiu, Michal Fečkan, JinRong Wang
• Date:
  2024.09.21
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 64, No 2 (December 2024); 441 - 469;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/55340/39784 ;https://apcz.umk.pl/TMNA/article/view/55340/39785
• Subject:
  PC-mild solutions;
  Caputo fractional derivative;
  impulsive conditions;
  evolution systems;
  Primary: 47J35, 26A33;
  Secondary: 34A37, 34A12
• Identifier: https://apcz.umk.pl/TMNA/article/view/55340
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other