Space-time fractional diffusion on bounded domains

Zhen Qing Chena; Mark M. Meerschaert; Erkan Nanec

doi:10.1016/j.jmaa.2012.04.032

Space-time fractional diffusion on bounded domains

Zhen Qing Chena, Mark M. Meerschaert^*, Erkan Nanec

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

105 Citations (Scopus)

Abstract

Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional diffusion equations on bounded domains, as well as probabilistic representations of these solutions, which are useful for particle tracking codes.

Original language	English
Pages (from-to)	479-488
Number of pages	10
Journal	Journal of Mathematical Analysis and Applications
Volume	393
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2012.04.032
Publication status	Published - 15 Sept 2012
Externally published	Yes

Keywords

Anomalous diffusion
Bounded domain
Cauchy problem
Fractional derivative
Probabilistic representation
Strong solution

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10.1016/j.jmaa.2012.04.032

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Chena, Z. Q., Meerschaert, M. M., & Nanec, E. (2012). Space-time fractional diffusion on bounded domains. Journal of Mathematical Analysis and Applications, 393(2), 479-488. https://doi.org/10.1016/j.jmaa.2012.04.032

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title = "Space-time fractional diffusion on bounded domains",

abstract = "Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional diffusion equations on bounded domains, as well as probabilistic representations of these solutions, which are useful for particle tracking codes.",

keywords = "Anomalous diffusion, Bounded domain, Cauchy problem, Fractional derivative, Probabilistic representation, Strong solution",

author = "Chena, {Zhen Qing} and Meerschaert, {Mark M.} and Erkan Nanec",

year = "2012",

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T1 - Space-time fractional diffusion on bounded domains

AU - Chena, Zhen Qing

AU - Meerschaert, Mark M.

AU - Nanec, Erkan

PY - 2012/9/15

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N2 - Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional diffusion equations on bounded domains, as well as probabilistic representations of these solutions, which are useful for particle tracking codes.

AB - Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional diffusion equations on bounded domains, as well as probabilistic representations of these solutions, which are useful for particle tracking codes.

KW - Anomalous diffusion

KW - Bounded domain

KW - Cauchy problem

KW - Fractional derivative

KW - Probabilistic representation

KW - Strong solution

UR - http://www.scopus.com/inward/record.url?scp=84860915044&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2012.04.032

DO - 10.1016/j.jmaa.2012.04.032

M3 - Article

AN - SCOPUS:84860915044

SN - 0022-247X

VL - 393

SP - 479

EP - 488

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Space-time fractional diffusion on bounded domains

Abstract

Keywords

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