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

Kamel Al-Khaled, Shaher Momani

Research output: Contribution to journalArticle

50 Citations (Scopus)

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 languageEnglish
Pages (from-to)473-483
Number of pages11
JournalApplied Mathematics and Computation
Volume165
Issue number2
DOIs
Publication statusPublished - Jun 15 2005

Fingerprint

Fractional Diffusion
Fractional Derivative
Wave equations
Decomposition Method
Diffusion equation
Wave equation
Approximate Solution
Decomposition
Derivatives
Diffusion Process
Partial differential equation
First-order
Derivative
Numerical Examples
Partial differential equations

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

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

In: Applied Mathematics and Computation, Vol. 165, No. 2, 15.06.2005, p. 473-483.

Research output: Contribution to journalArticle

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