On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order
type: Item
instance of: scholarly article
title: On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order
zbMATH Open document ID: 1207.45014
author: Bashir Ahmad
author: Seenith Sivasundaram
published in: Applied Mathematics and Computation
publication date: 2010-10-25T00:00:00Z
review text: The authors consider the four-point nonlocal boundary value problem in a Banach space \(X\), i.e. \[ ^cD^qx(t)=f(t,x(t),(\phi x)(t),(\psi x)(t)),\;\;0<t<1, \;\;1<q<2, \] \[ x'(0)+ax(\eta_1)=0, \;\;bx'(1)+x(\eta_2)=0,\;\;0<\eta_1\leq \eta_2<1, \] where \(^cD\) is the Caputo's fractional derivative, \(f:[0,1]\times X\times X\times X\times X\to X\) is continuous, \(\phi\), \(\psi\) are Volterra integral operators and \(a,c\in (0,1)\). By using fixed point arguments they prove an existence and uniqueness result of solutions for the problem above.
Mathematics Subject Classification ID: 45N05
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 45G10
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 5804902
zbMATH Keywords: nonlinear fractional differential equations
zbMATH Keywords: nonlocal boundary conditions
zbMATH Keywords: fixed point arguments
zbMATH Keywords: Banach space
zbMATH Keywords: Volterra integral operators
reviewed by: Ioan I. Vrabie
MaRDI profile type: Publication
full work available at URL: j.amc.2010.05.080
OpenAlex ID: W2125690132
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DOI: 10.1016/J.AMC.2010.05.080
description: scientific article; zbMATH DE number 5804902