Analytical approach to Boussinesq equation with space- and time-fractional derivatives

In this paper, the homotopy perturbation method (HPM) is developed to obtain approximate analytical solutions of a fractional Boussinesq equation with initial condition. The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made, the comparisons sh...

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Bibliographic Details
Published in:International journal for numerical methods in fluids 2011-08, Vol.66 (10), p.1315-1324
Main Authors: Yıldırım, Ahmet, Sezer, Sefa Anıl, Kaplan, Yasemin
Format: Article
Language:English
Subjects:
Approximation
Boussinesq equations
Caputo sense
Computational fluid dynamics
Derivatives
Exact sciences and technology
Fluid dynamics
fractional Boussinesq equation
Fundamental areas of phenomenology (including applications)
General theory
homotopy perturbation method
Initial conditions
Mathematical analysis
Mathematical models
Perturbation methods
Physics
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Summary:In this paper, the homotopy perturbation method (HPM) is developed to obtain approximate analytical solutions of a fractional Boussinesq equation with initial condition. The fractional derivatives are described in the Caputo sense. Some examples are given and comparisons are made, the comparisons show that the HPM is very effective and convenient and overcomes the difficulty of traditional methods. The numerical results show that the approaches are easy to implement and accurate when applied to space‐ and time‐fractional equations. Copyright © 2010 John Wiley & Sons, Ltd.
ISSN:0271-2091
1097-0363
1097-0363
DOI:10.1002/fld.2315