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Abundant new solutions of the transmission of nerve impulses of an excitable system

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Abstract

This research investigates the dynamical behavior of the transmission of nerve impulses of a nervous system (the neuron) by studying the computational solutions of the FitzHugh–Nagumo equation that is used as a model of the transmission of nerve impulses. For achieving our goal, we employ two recent computational schemes (the extended simplest equation method and Sinh–Cosh expansion method) to evaluate some novel computational solutions of these models. Moreover, we study the stability property of the obtained solutions to show the applicability of them in life. For more explanation of this transmission, some sketches are given for the analytical obtained solutions. A comparison between our results and that obtained in previous work is also represented and discussed in detail to show the novelty for our solutions. The performance of the two used methods shows power, practical and their ability to apply to other nonlinear partial differential equations.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Jiangsu University, Zhenjiang, China

    Mostafa M. A. Khater & Raghda A. M. Attia

  2. Department of Basic Science, Higher Technological Institute, 10th of Ramadan City, Egypt

    Raghda A. M. Attia

  3. Department of Mathematics, Cankaya University, Ankara, Turkey

    Dumitru Baleanu

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

    Dumitru Baleanu

Authors
  1. Mostafa M. A. Khater
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  2. Raghda A. M. Attia
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  3. Dumitru Baleanu
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Correspondence to Mostafa M. A. Khater.

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Khater, M.M.A., Attia, R.A.M. & Baleanu, D. Abundant new solutions of the transmission of nerve impulses of an excitable system. Eur. Phys. J. Plus 135, 251 (2020). https://doi.org/10.1140/epjp/s13360-020-00261-7

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