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Homotopy Perturbation Method for Solving Time Fractional Coupled Viscous Burgers’ Equation in \((2+1)\) and \((3+1)\) Dimensions

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Abstract

This paper deals with an approximate analytical solution of multi-dimensional, time-fractional coupled viscous Burgers’ equation obtained by employing “homotopy perturbation method” where fractional derivative is of Caputo type. Three test problems are carried out in order to validate and illustrate the efficiency of the method for TFCB equation. The results are also depicted in graphically for different values of fractional order \(\alpha \) and Reynolds number. It is found that the proposed series solutions converges rapidly for large Reynolds numbers (Re \(\ge 100\)).

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Acknowledgements

The authors are grateful to the anonymous referees for their time, effort, and extensive comments which improve the quality of the presentation of the paper. Pramod Kumar also thankful to Babasaheb Bhimrao Ambedkar University, Lucknow, INDIA for financial assistance to carry out the work.

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Authors and Affiliations

  1. Department of Mathematics, School of Physical and Decision Sciences, Babasaheb Bhimrao Ambedkar University, Lucknow, Uttar Pradesh, 226 025, India

    Brajesh Kumar Singh, Pramod Kumar & Vineet Kumar

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  1. Brajesh Kumar Singh
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  2. Pramod Kumar
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  3. Vineet Kumar
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Correspondence to Brajesh Kumar Singh.

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Singh, B.K., Kumar, P. & Kumar, V. Homotopy Perturbation Method for Solving Time Fractional Coupled Viscous Burgers’ Equation in \((2+1)\) and \((3+1)\) Dimensions. Int. J. Appl. Comput. Math 4, 38 (2018). https://doi.org/10.1007/s40819-017-0469-3

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  • DOI: https://doi.org/10.1007/s40819-017-0469-3

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