Publication result detail

Applications of the fractional calculus: On a discretization of fractional diffusion equation in one dimension

KISELA, T.

Original Title

Applications of the fractional calculus: On a discretization of fractional diffusion equation in one dimension

English Title

Applications of the fractional calculus: On a discretization of fractional diffusion equation in one dimension

Type

Peer-reviewed article not indexed in WoS or Scopus

Original Abstract

The paper discusses the problem of the classical and fractional diffusion models. It is known that the classical one fails in heterogeneous structures with locations where particles move with a large speed for a long distance. If we replace the second derivative in the space variable in the classical diffusion equation by a fractional derivative of order less than two, we obtain the fractional diffusion equation (FDE) which is more useful in this case. In this paper we introduce a discretization of FDE based on the theory of the difference fractional calculus and we sketch a basic numerical scheme of its solving. Finally, we present some examples comparing classical and fractional diffusion models.

English abstract

The paper discusses the problem of the classical and fractional diffusion models. It is known that the classical one fails in heterogeneous structures with locations where particles move with a large speed for a long distance. If we replace the second derivative in the space variable in the classical diffusion equation by a fractional derivative of order less than two, we obtain the fractional diffusion equation (FDE) which is more useful in this case. In this paper we introduce a discretization of FDE based on the theory of the difference fractional calculus and we sketch a basic numerical scheme of its solving. Finally, we present some examples comparing classical and fractional diffusion models.

Keywords

fractional diffusion equation, numerical solution, discrete fractional calculus

Key words in English

fractional diffusion equation, numerical solution, discrete fractional calculus

Authors

KISELA, T.

RIV year

2010

Released

01.03.2010

Publisher

EDIS - Publishing Institution of Zilina University

ISBN

1335-4205

Periodical

Communications

Volume

12

Number

1

State

Slovak Republic

Pages from

5

Pages to

11

Pages count

7

URL

http://www.uniza.sk/komunikacie/archiv/2010/1/1_2010en.pdf

BibTex

@article{BUT48211,
  author="Tomáš {Kisela}",
  title="Applications of the fractional calculus: On a discretization of fractional diffusion equation in one dimension",
  journal="Communications",
  year="2010",
  volume="12",
  number="1",
  pages="5--11",
  issn="1335-4205",
  url="http://www.uniza.sk/komunikacie/archiv/2010/1/1_2010en.pdf"
}