A nonstandard finite difference scheme for two-sided space-fractional partial differential equations

Shaher Momani; Abdullah Abu Rqayiq; Dumitru Baleanu

doi:10.1142/S0218127412500794

A nonstandard finite difference scheme for two-sided space-fractional partial differential equations

Shaher Momani
, Abdullah Abu Rqayiq
, Dumitru Baleanu

University of Jordan
University of Mutah
Cankaya University
Institute for Space Sciences

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

26 Scopus citations

Abstract

In this paper, we apply the Mickens nonstandard discretization method to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and thereby increase the accuracy of the solutions. We examine the case when a left-handed and a right-handed fractional spatial derivative may be present in the partial differential equation. Two numerical examples using this method are presented and compared successfully with the exact analytical solutions.

Original language	English
Article number	1250079
Journal	International Journal of Bifurcation and Chaos
Volume	22
Issue number	4
DOIs	https://doi.org/10.1142/S0218127412500794
State	Published - Apr 2012
Externally published	Yes

Keywords

Fractional differential equations
left-handed fractional derivative
nonstandard finite difference schemes
right-handed fractional derivative

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10.1142/S0218127412500794

Cite this

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abstract = "In this paper, we apply the Mickens nonstandard discretization method to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and thereby increase the accuracy of the solutions. We examine the case when a left-handed and a right-handed fractional spatial derivative may be present in the partial differential equation. Two numerical examples using this method are presented and compared successfully with the exact analytical solutions.",

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N2 - In this paper, we apply the Mickens nonstandard discretization method to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and thereby increase the accuracy of the solutions. We examine the case when a left-handed and a right-handed fractional spatial derivative may be present in the partial differential equation. Two numerical examples using this method are presented and compared successfully with the exact analytical solutions.

AB - In this paper, we apply the Mickens nonstandard discretization method to solve a class of initial-boundary value fractional partial differential equations with variable coefficients on a finite domain, and thereby increase the accuracy of the solutions. We examine the case when a left-handed and a right-handed fractional spatial derivative may be present in the partial differential equation. Two numerical examples using this method are presented and compared successfully with the exact analytical solutions.

KW - Fractional differential equations

KW - left-handed fractional derivative

KW - nonstandard finite difference schemes

KW - right-handed fractional derivative

UR - https://www.scopus.com/pages/publications/84861220180

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M3 - Article

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ER -

A nonstandard finite difference scheme for two-sided space-fractional partial differential equations

Abstract

Keywords

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