### Abstract

A non-standard finite difference scheme is developed to solve the linear partial differential equations with time- and space-fractional derivatives. The GrunwaldLetnikov method is used to approximate the fractional derivatives. Numerical illustrations that include the linear inhomogeneous time-fractional equation, linear space-fractional telegraph equation, linear inhomogeneous fractional Burgers equation and the fractional wave equation are investigated to show the pertinent features of the technique. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is very effective and convenient for solving linear partial differential equations of fractional order.

Original language | English |
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Pages (from-to) | 1209-1216 |

Number of pages | 8 |

Journal | Computers and Mathematics with Applications |

Volume | 61 |

Issue number | 4 |

DOIs | |

Publication status | Published - Feb 2011 |

### Fingerprint

### Keywords

- Burgers equation
- Fractional differential equations
- Non-standard finite difference schemes
- Telegraph equation
- Wave equation

### ASJC Scopus subject areas

- Computational Theory and Mathematics
- Modelling and Simulation
- Computational Mathematics

### Cite this

*Computers and Mathematics with Applications*,

*61*(4), 1209-1216. https://doi.org/10.1016/j.camwa.2010.12.072

**The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics.** / Moaddy, K.; Momani, S.; Hashim, Ishak.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 61, no. 4, pp. 1209-1216. https://doi.org/10.1016/j.camwa.2010.12.072

}

TY - JOUR

T1 - The non-standard finite difference scheme for linear fractional PDEs in fluid mechanics

AU - Moaddy, K.

AU - Momani, S.

AU - Hashim, Ishak

PY - 2011/2

Y1 - 2011/2

N2 - A non-standard finite difference scheme is developed to solve the linear partial differential equations with time- and space-fractional derivatives. The GrunwaldLetnikov method is used to approximate the fractional derivatives. Numerical illustrations that include the linear inhomogeneous time-fractional equation, linear space-fractional telegraph equation, linear inhomogeneous fractional Burgers equation and the fractional wave equation are investigated to show the pertinent features of the technique. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is very effective and convenient for solving linear partial differential equations of fractional order.

AB - A non-standard finite difference scheme is developed to solve the linear partial differential equations with time- and space-fractional derivatives. The GrunwaldLetnikov method is used to approximate the fractional derivatives. Numerical illustrations that include the linear inhomogeneous time-fractional equation, linear space-fractional telegraph equation, linear inhomogeneous fractional Burgers equation and the fractional wave equation are investigated to show the pertinent features of the technique. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is very effective and convenient for solving linear partial differential equations of fractional order.

KW - Burgers equation

KW - Fractional differential equations

KW - Non-standard finite difference schemes

KW - Telegraph equation

KW - Wave equation

UR - http://www.scopus.com/inward/record.url?scp=79651469164&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79651469164&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2010.12.072

DO - 10.1016/j.camwa.2010.12.072

M3 - Article

AN - SCOPUS:79651469164

VL - 61

SP - 1209

EP - 1216

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 4

ER -