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A new numerical algorithm for fractional Fitzhugh–Nagumo equation arising in transmission of nerve impulses

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Abstract

The principal objective of this study is to present a new numerical scheme based on a combination of q-homotopy analysis approach and Laplace transform approach to examine the Fitzhugh–Nagumo (F–N) equation of fractional order. The F–N equation describes the transmission of nerve impulses. In order to handle the nonlinear terms, the homotopy polynomials are employed. To validate the results derived by employing the used scheme, we study the F–N equation of arbitrary order by using the fractional reduced differential transform scheme. The error analysis of the proposed approach is also discussed. The outcomes are shown through the graphs and tables that elucidate that the used schemes are very fantastic and accurate.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions to improve the final version of the article.

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Authors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, Rajasthan, 303905, India

    Devendra Kumar & Jagdev Singh

  2. Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, Eskisehir Yolu 29. Km, Yukarıyurtcu Mahallesi Mimar Sinan Caddesi No: 4, 06790, Etimesgut, Turkey

    Dumitru Baleanu

  3. Institute of Space Sciences, Magurele, Bucharest, Romania

    Dumitru Baleanu

Authors
  1. Devendra Kumar
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  2. Jagdev Singh
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  3. Dumitru Baleanu
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Correspondence to Devendra Kumar.

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Kumar, D., Singh, J. & Baleanu, D. A new numerical algorithm for fractional Fitzhugh–Nagumo equation arising in transmission of nerve impulses. Nonlinear Dyn 91, 307–317 (2018). https://doi.org/10.1007/s11071-017-3870-x

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  • DOI: https://doi.org/10.1007/s11071-017-3870-x

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