On the solutions of a nonlinear fractional integro-differential equation of pantograph type
type: Item
instance of: scholarly article
title: On the solutions of a nonlinear fractional integro-differential equation of pantograph type
zbMATH Open document ID: 1382.65468
author: Peng Zhang
published in: Mediterranean Journal of Mathematics
publication date: 2017-11-09T00:00:00Z
review text: This article considers a fractional integro-differential equation on \([0,T]\) of the form \[ D^\alpha u(t) = f(t,u(t),u(pt)) + \int_0^{qt} g_1(t,s,u(s)) \,ds + \int_0^t g_2(t,s,u(s)) \,dx, \] where \(0 < \alpha, p, q < 1\), \(D^\alpha\) is the Caputo fractional derivative, and \(f\), \(g_1\), \(g_2\) are continuous. The authors first prove the existence and uniqueness of the solution, and then present a numerical method based on sinc functions. Some numerical examples are given.
reviewed by: Fritz Keinert
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45J05
Mathematics Subject Classification ID: 26A33
Mathematics Subject Classification ID: 45G10
zbMATH DE Number: 6804290
zbMATH Keywords: fractional integro-differential equation
zbMATH Keywords: pantograph equation
zbMATH Keywords: sinc collocation
zbMATH Keywords: numerical example
describes a project that uses: Sinc-Pack
MaRDI profile type: Publication
full work available at URL: s00009-017-0993-8
OpenAlex ID: W2751433614
Wikidata QID: Q115390346
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DOI: 10.1007/S00009-017-0993-8
description: scientific article; zbMATH DE number 6804290