Detail publikace

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

KISELA, T.

Anglický název

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

Typ

Článek recenzovaný mimo WoS a Scopus

Jazyk

en

Originální abstrakt

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.

Klíčová slova anglicky

fractional diffusion equation, numerical solution, discrete fractional calculus

Vydáno

2010-03-01

Nakladatel

EDIS – Publishing Institution of Zilina University

ISSN

1335-4205

Časopis

Komunikacie – vedecke listy Zilinskej univerzity v Ziline

Ročník

12

Číslo

1

Strany od–do

5–11

Počet stran

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"
}