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 |
Externally published | Yes |
Keywords
- Decomposition method
- Diffusion-wave equation
- Fractional calculus
- Heat equation
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics