An algorithm for the numerical solution of differential equations of fractional order
type: Item
instance of: scholarly article
title: An algorithm for the numerical solution of differential equations of fractional order
zbMATH Open document ID: 0890.65071
author: Kai Diethelm
publication date: 1998-03-15T00:00:00Z
full work available at URL: https://eudml.org/doc/119480
full work available at URL: pp1-6.html
review text: The author considers the fractional differential equation \[ (D^q[x-x_0])(t)=\beta x(t)+f(t), \qquad 0\leq t \leq 1, \quad x(0)=x_0, \] where \(0<q<1\), \(f\) is a given function on the interval \([0,1]\), \(\beta \leq 0\). Here \(D^q x\) denotes the Riemann-Liouville fractional derivative of order \(q\). An implicit algorithm for the approximate solution of an important class of these equations is proposed. Error estimates and numerical examples are given.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 26A33
zbMATH DE Number: 1128742
zbMATH Keywords: fractional differential equation
zbMATH Keywords: Riemann-Liouville fractional derivative
zbMATH Keywords: numerical examples
zbMATH Keywords: error estimates
zbMATH Keywords: implicit algorithm
reviewed by: S. Yanchuk
MaRDI profile type: Publication
published in: ETNA - Electronic Transactions on Numerical Analysis
description: scientific article; zbMATH DE number 1128742