Application of Homotopy Perturbation Transform Method to Linear and Non-linear Space-time Fractional Reaction-diffusion Equations

Volume 5, Issue 1, pp 40-52 http://dx.doi.org/10.22436/jmcs.05.01.05

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Authors

Jagdev Singh - Department of Mathematics, Jagan Nath University, Jaipur, Rajasthan, India. Devendra Kumar - Department of Mathematics, Jagan Nath Gupta Inst. of Engg. & Tech., Jaipur, Rajasthan, India. Sushila - Department of Physics, Jagan Nath University, Jaipur, Rajasthan, India Sumit Gupta - Department of Mathematics, Jagan Nath Gupta Inst. of Engg. & Tech., Jaipur, Rajasthan, India.

Abstract

In this paper, we obtain the analytical solutions of linear and non-linear space-time fractional reaction-diffusion equations on a finite domain by the application of homotopy perturbation transform method (HPTM). The HPTM is a combined form of the Laplace transform method with the homotopy perturbation method. Some examples are also given. Numerical results show that the HPTM is easy to implement and accurate when applied to linear and non-linear space-time fractional reaction-diffusion equations.

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Keywords

• Homotopy perturbation transform method
• Laplace transform
• fractional reaction-diffusion equation
• Caputo time-fractional derivative
• Caputo space-fractional derivative.

MSC

•  35K57
•  35B20
•  65H20

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