Analytical approximate solutions of the fractional convection–diffusion equation with nonlinear source term by He's homotopy perturbation method

Abstract

In this study, we present a framework to obtain analytical approximate solutions to the nonlinear fractional convection–diffusion equation. The fractional derivative is considered in the Caputo sense. The applications of the homotopy perturbation method were extended to derive analytical solutions in the form of a series with easily computed terms for this equation. Some examples are tested and the results reveal that the technique introduced here is very effective and convenient for solving nonlinear partial differential equations of fractional order.

Keywords:

• homotopy perturbation method
• convection–diffusion equation
• Caputo fractional derivative
• fractional differential equations

2000 AMS Subject Classifications::

• 26A33
• 34K28
• 65N99
• 33F05
• 82B80

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Correction

Notes

This article was originally published with errors, which have now been corrected in the online version. Please see Correction (http://dx.doi.org/10.1080/00207160903023581).