Publication detail

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

KISELA, T.

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

Language

en

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.

Keywords in English

fractional diffusion equation, numerical solution, discrete fractional calculus

Released

2010-03-01

Publisher

EDIS – Publishing Institution of Zilina University

ISSN

1335-4205

Journal

Komunikacie – vedecke listy Zilinskej univerzity v Ziline

Volume

12

Number

1

Pages from–to

5–11

Pages count

7

BIBTEX


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