Description

• Title:
  Fixed point results in set $P_{h,e}$ with applications to fractional differential equations
• Creator:
  Zhang, Lingling;
  Wang, Hui;
  Wang, Xiaoqiang
• Description:
  In this paper, without assuming operators to be continuous or compact, by employing monotone iterative technique on ordered Banach space, we at first establish new fixed point theorems for some kinds of nonlinear mixed monotone operators in set $P_{h,e}$. Then, we study a new form of fractional two point boundary value problem depending on a certain constant and give the existence and uniqueness of solutions. We also show that the unique solution exists in set $P_{h,e}$ or $P_{h}$ and can be uniformly approximated by constructing two iterative sequences for any initial values. At the end, a concrete example is given to illustrate our abstract results. The conclusions of this article enrich the fixed point theorems and provide new methods to deal with nonlinear differential equations.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.10.06
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 54, No 2 (December 2019); 536 - 566;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.052/18478 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.052/18479
• Subject:
  Fixed point theorem;
  mixed monotone operator;
  set $P_{h;
  e}$;
  existence and uniqueness;
  fractional differential equations;
  47H10;
  47H07;
  34A08;
  34B15
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.052
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other