### Abstract

The partial differential equation of diffusion is generalized by replacing the first order time derivative by a fractional derivative of order α, 0 <α ≤ 2. An approximate solution based on the decomposition method is given for the generalized fractional diffusion (diffusion-wave) equation. The fractional derivative is described in the Caputo sense. Numerical example is given to show the application of the present technique. Results show the transition from a pure diffusion process (α = 1) to a pure wave process (α = 2).

Original language | English |
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Pages (from-to) | 473-483 |

Number of pages | 11 |

Journal | Applied Mathematics and Computation |

Volume | 165 |

Issue number | 2 |

DOIs | |

Publication status | Published - Jun 15 2005 |

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### Keywords

- Decomposition method
- Diffusion-wave equation
- Fractional calculus
- Heat equation

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

### Cite this

*Applied Mathematics and Computation*,

*165*(2), 473-483. https://doi.org/10.1016/j.amc.2004.06.026

**An approximate solution for a fractional diffusion-wave equation using the decomposition method.** / Al-Khaled, Kamel; Momani, Shaher.

Research output: Contribution to journal › Article

*Applied Mathematics and Computation*, vol. 165, no. 2, pp. 473-483. https://doi.org/10.1016/j.amc.2004.06.026

}

TY - JOUR

T1 - An approximate solution for a fractional diffusion-wave equation using the decomposition method

AU - Al-Khaled, Kamel

AU - Momani, Shaher

PY - 2005/6/15

Y1 - 2005/6/15

N2 - The partial differential equation of diffusion is generalized by replacing the first order time derivative by a fractional derivative of order α, 0 <α ≤ 2. An approximate solution based on the decomposition method is given for the generalized fractional diffusion (diffusion-wave) equation. The fractional derivative is described in the Caputo sense. Numerical example is given to show the application of the present technique. Results show the transition from a pure diffusion process (α = 1) to a pure wave process (α = 2).

AB - The partial differential equation of diffusion is generalized by replacing the first order time derivative by a fractional derivative of order α, 0 <α ≤ 2. An approximate solution based on the decomposition method is given for the generalized fractional diffusion (diffusion-wave) equation. The fractional derivative is described in the Caputo sense. Numerical example is given to show the application of the present technique. Results show the transition from a pure diffusion process (α = 1) to a pure wave process (α = 2).

KW - Decomposition method

KW - Diffusion-wave equation

KW - Fractional calculus

KW - Heat equation

UR - http://www.scopus.com/inward/record.url?scp=17644372361&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17644372361&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2004.06.026

DO - 10.1016/j.amc.2004.06.026

M3 - Article

VL - 165

SP - 473

EP - 483

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

IS - 2

ER -