Publication detail
On a Discretization of the Initial Value Problem for a Linear Nonhomogeneous Fractional Differential Equation
KISELA, T.
Czech title
O diskretizaci počátečního problému pro lineární nehomogenní zlomkovou diferenciální rovnici
English title
On a Discretization of the Initial Value Problem for a Linear Nonhomogeneous Fractional Differential Equation
Type
conference paper
Language
en
Original abstract
Fractional differential equations with Riemann-Liouville differential operator appear in many applications. Considering these problems, initial or boundary conditions are naturally given via noninteger order integrals and derivatives. In this paper we focus on a test linear initial-value problem with Riemann-Liouville fractional derivative. We are going to introduce a discretization of this problem which allows to involve initial conditions of a noninteger order. We illustrate it by a few examples.
Czech abstract
Zlomkové diferenciální rovnice s Riemann-Liouvilleovým operátorem se vyskytují v mnoha aplikacích. Pro problémy tohoto typu jsou počáteční a okrajové podmínky přirozeně dány formou integrálů a derivací neceločíselných řádů. V tomto článku se zaměříme na testovací počáteční problém s Riemann-Liouvilleovou zlomkovou derivací. Uvedeme diskretizaci této úlohy umožňující zahrnout počáteční podmínky neceločíselných řádů. Vše ilustrujeme na příkladech.
English abstract
Fractional differential equations with Riemann-Liouville differential operator appear in many applications. Considering these problems, initial or boundary conditions are naturally given via noninteger order integrals and derivatives. In this paper we focus on a test linear initial-value problem with Riemann-Liouville fractional derivative. We are going to introduce a discretization of this problem which allows to involve initial conditions of a noninteger order. We illustrate it by a few examples.
Keywords in Czech
Riemann-Liouvilleův operátor, počáteční problém, diskretizace, sekvenční algoritmus
Keywords in English
Riemann-Liouville operator, initial-value problem, discretization, sequential algorithms
RIV year
2010
Released
18.10.2010
Publisher
Technical University of Kosice and University of Extremadura
Location
Badajoz, Španělsko
ISBN
978-80-553-0487-8
Book
Proceedings of FDA'10
Pages from–to
264–269
Pages count
6
BIBTEX
@inproceedings{BUT34721,
author="Tomáš {Kisela},
title="On a Discretization of the Initial Value Problem for a Linear Nonhomogeneous Fractional Differential Equation",
booktitle="Proceedings of FDA'10",
year="2010",
month="October",
pages="264--269",
publisher="Technical University of Kosice and University of Extremadura",
address="Badajoz, Španělsko",
isbn="978-80-553-0487-8"
}