Detail publikačního výsledku

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

KISELA, T.

Originální název

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

Anglický název

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

Druh

Článek recenzovaný mimo WoS a Scopus

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.

Anglický 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

fractional diffusion equation, numerical solution, discrete fractional calculus

Klíčová slova v angličtině

fractional diffusion equation, numerical solution, discrete fractional calculus

Autoři

KISELA, T.

Rok RIV

2010

Vydáno

01.03.2010

Nakladatel

EDIS - Publishing Institution of Zilina University

ISSN

1335-4205

Periodikum

Communications

Svazek

12

Číslo

1

Stát

Slovenská republika

Strany od

5

Strany do

11

Strany počet

7

URL

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

Plný text v Digitální knihovně

http://hdl.handle.net/

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"
}