Existence results for \((n-1,1)\)-type nonlocal integral boundary value problems for coupled systems of fractional differential equations at resonance
type: Item
instance of: scholarly article
title: Existence results for \((n-1,1)\)-type nonlocal integral boundary value problems for coupled systems of fractional differential equations at resonance
zbMATH Open document ID: 1395.34004
author: Lei Hu
published in: Journal of Applied Mathematics and Computing
publication date: 2018-04-13T00:00:00Z
review text: Consider the boundary value problem \[ \begin{aligned} D^\alpha_{0+}u &= f(t,v,v',\dots, v^{(n-1)}),\quad 0<t<1,\\ D^\beta_{0+}v &= g(t,\breve u,\breve u',\dots, \breve u^{(n-1)}),\quad 0<t<1,\\ u^{(i)}(0) &= v^{(i)}(0)= 0\quad\text{for }0\leq i\leq n-2,\\ u(1) &= \lambda\int^\eta_0 u(t)\,dt,\quad v(1)= \mu\int^\xi_0 v(t)\,dt,\end{aligned}\tag{\(*\)} \] where \(n-1<\alpha\), \(\beta<n\), \(n\geq 2\), \(D^\alpha_{0+}\) and \(D^\beta_{0+}\) denote the Caputo fractional derivative, \(f,g:[0,1]\times \mathbb{R}^n\to\mathbb{R}\) are continuous functions, and \(\eta,\xi\in[0,1]\) are given constants satisfying \(\lambda\eta^n= \mu\xi^n=n\). The author studies \((*)\) by means of the coincidence theory.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6859487
zbMATH Keywords: fractional differential equation
zbMATH Keywords: integral boundary conditions
zbMATH Keywords: coincidence degree theory
zbMATH Keywords: resonance
MaRDI profile type: Publication
full work available at URL: s12190-016-1075-y
OpenAlex ID: W2560684538
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DOI: 10.1007/S12190-016-1075-Y
description: scientific article; zbMATH DE number 6859487