### 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 |

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Numerical Analysis

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## Cite this

Al-Khaled, K., & Momani, S. (2005). An approximate solution for a fractional diffusion-wave equation using the decomposition method.

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