Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method

Shaher Momani

doi:10.1016/j.amc.2004.06.025

Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method

Shaher Momani

United Arab Emirates University

Research output: Contribution to journal › Article › peer-review

100 Scopus citations

Abstract

The time fractional heat-like and wave-like equations with variable coefficients are obtained by replacing the first order and second order time derivative by a fractional derivative of order α, 0 < α ≤ 2. The applications of the decomposition method were extended to derive analytical solutions in the form of a series with easily computed terms for these generalized fractional equation. Some examples are presented to show the efficiency and simplicity of the method.

Original language	English
Pages (from-to)	459-472
Number of pages	14
Journal	Applied Mathematics and Computation
Volume	165
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2004.06.025
State	Published - 15 Jun 2005
Externally published	Yes

Keywords

Decomposition method
Fractional calculus
Heat-like equation
Wave-like equation

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10.1016/j.amc.2004.06.025

Cite this

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abstract = "The time fractional heat-like and wave-like equations with variable coefficients are obtained by replacing the first order and second order time derivative by a fractional derivative of order α, 0 < α ≤ 2. The applications of the decomposition method were extended to derive analytical solutions in the form of a series with easily computed terms for these generalized fractional equation. Some examples are presented to show the efficiency and simplicity of the method.",

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AB - The time fractional heat-like and wave-like equations with variable coefficients are obtained by replacing the first order and second order time derivative by a fractional derivative of order α, 0 < α ≤ 2. The applications of the decomposition method were extended to derive analytical solutions in the form of a series with easily computed terms for these generalized fractional equation. Some examples are presented to show the efficiency and simplicity of the method.

KW - Decomposition method

KW - Fractional calculus

KW - Heat-like equation

KW - Wave-like equation

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JO - Applied Mathematics and Computation

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ER -

Analytical approximate solution for fractional heat-like and wave-like equations with variable coefficients using the decomposition method

Abstract

Keywords

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