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Fractional transform methods for coupled system of time fractional derivatives of non-homogeneous Burgers’ equations arise in diffusive effects

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Abstract

The coupled system of time fractional derivatives of non-homogeneous Burgers’ equations is solved both analytically and numerically. The approximate analytical solutions of power series type are obtained by the fractional homotopy analysis transform method, which is verified numerically by the coupled fractional reduced differential transform method. Particularly, the present analytical solutions are compared with the results available in the literature for several special cases, and very excellent agreement was found. An error analysis is done to compute the average squared residual errors of those analytical approximations for other cases. The present analysis shows that the proposed technique has very excellent efficiency to give solutions with high precision. On the other hand, it is found that the optimal convergence control parameter derived here not only controls the convergence of the present solutions but also leads to identifying multiple solutions.

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Acknowledgements

The author express his heartfelt thanks to the reviewers for their valuable suggestions for the improvement of the article.

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  1. Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, South Ambazari Road, Nagpur, Maharashtra, 440010, India

    Shankar Rao Munjam

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  1. Shankar Rao Munjam
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Correspondence to Shankar Rao Munjam.

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Communicated by Vasily E. Tarasov.

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Munjam, S.R. Fractional transform methods for coupled system of time fractional derivatives of non-homogeneous Burgers’ equations arise in diffusive effects. Comp. Appl. Math. 38, 62 (2019). https://doi.org/10.1007/s40314-019-0829-1

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  • DOI: https://doi.org/10.1007/s40314-019-0829-1

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