Description

• Title:
  Impulsive problems for fractional evolution equations and optimal controls in infinite dimensional spaces
• Creator:
  Wang, JinRong;
  Zhou, Yong;
  Wei, Wei
• Description:
  In this paper, a class of impulsive fractional evolution equations and optimal controls in infinite dimensional spaces is considered. A suitable concept of a $PC$-mild solution is introduced and a suitable operator mapping is also constructed. By using a $PC$-type Ascoli-Arzela theorem, the compactness of the operator mapping is proven. Applying a generalized Gronwall inequality and Leray-Schauder fixed point theorem, the existence and uniqueness of the $PC$-mild solutions is obtained. Existence of optimal pairs for system governed by impulsive fractional evolution equations is also presented. Finally, an example illustrates the applicability of our results.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2016 Topological Methods in Nonlinear Analysis
• Date:
  2011.04.23
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 38, No 1 (September 2011); 17 - 43;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.022/8410
• Subject:
  Impulsive fractional evolution equations;
  $PC$-mild solutions;
  compactness;
  existence;
  continuous dependence;
  optimal controls;
  26A33;
  34A12;
  34A37;
  47J35;
  93C10;
  93C25
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2011.022
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other