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Novel Exact Soliton Solutions of Cahn–Allen Models with Truncated M-fractional Derivative

Received: 20 September 2022     Accepted: 7 November 2022     Published: 29 December 2022
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Abstract

In recent research the effect of different type fractional derivative to nonlinear evolution equations plays a vital rule in the various branches of science and engineering. The nonlinear physical phenomena are expressed by nonlinear partial differential equations which are characteristics on the field of solid-state physics, plasma physics, fluid mechanics, chemical physics, mechanics, biology, chemistry, and so on. To visualize and identify their properties, it is essential to find the exact and multi solitons of the related nonlinear partial differential equation. In this work, we investigate more soliton solutions for novel truncated M-fractional Cahn–Allen (t-MfCA) models to secure different soliton solutions via the unified scheme. This model has significant in the area of mathematical physics and also known as reaction–diffusion. The obtained solutions are expressed in turns of trigonometric, hyperbolic and rational function solution under the condition on the free constraints. This work offers the kink, singular soliton, different type interaction of kink and lump wave for the numerical value of the free constraints. Form the obtained solution it is shown that the implement method is more informal, effective and reliable as compared to other methods. The calculation and all analytic solutions are verified by computational software MAPLE 18.

Published in International Journal of Theoretical and Applied Mathematics (Volume 8, Issue 6)
DOI 10.11648/j.ijtam.20220806.11
Page(s) 112-120
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2022. Published by Science Publishing Group

Keywords

Cahn–Allen Models, Unified Scheme, Reaction–Diffusion

References
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Cite This Article
  • APA Style

    Mohammad Mobarak Hossain, Md. Mamunur Roshid, Md. Abu Naim Sheikh, Mohammad Abu Taher, Harun-Or-Roshid. (2022). Novel Exact Soliton Solutions of Cahn–Allen Models with Truncated M-fractional Derivative. International Journal of Theoretical and Applied Mathematics, 8(6), 112-120. https://doi.org/10.11648/j.ijtam.20220806.11

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    ACS Style

    Mohammad Mobarak Hossain; Md. Mamunur Roshid; Md. Abu Naim Sheikh; Mohammad Abu Taher; Harun-Or-Roshid. Novel Exact Soliton Solutions of Cahn–Allen Models with Truncated M-fractional Derivative. Int. J. Theor. Appl. Math. 2022, 8(6), 112-120. doi: 10.11648/j.ijtam.20220806.11

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    AMA Style

    Mohammad Mobarak Hossain, Md. Mamunur Roshid, Md. Abu Naim Sheikh, Mohammad Abu Taher, Harun-Or-Roshid. Novel Exact Soliton Solutions of Cahn–Allen Models with Truncated M-fractional Derivative. Int J Theor Appl Math. 2022;8(6):112-120. doi: 10.11648/j.ijtam.20220806.11

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  • @article{10.11648/j.ijtam.20220806.11,
      author = {Mohammad Mobarak Hossain and Md. Mamunur Roshid and Md. Abu Naim Sheikh and Mohammad Abu Taher and Harun-Or-Roshid},
      title = {Novel Exact Soliton Solutions of Cahn–Allen Models with Truncated M-fractional Derivative},
      journal = {International Journal of Theoretical and Applied Mathematics},
      volume = {8},
      number = {6},
      pages = {112-120},
      doi = {10.11648/j.ijtam.20220806.11},
      url = {https://doi.org/10.11648/j.ijtam.20220806.11},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijtam.20220806.11},
      abstract = {In recent research the effect of different type fractional derivative to nonlinear evolution equations plays a vital rule in the various branches of science and engineering. The nonlinear physical phenomena are expressed by nonlinear partial differential equations which are characteristics on the field of solid-state physics, plasma physics, fluid mechanics, chemical physics, mechanics, biology, chemistry, and so on. To visualize and identify their properties, it is essential to find the exact and multi solitons of the related nonlinear partial differential equation. In this work, we investigate more soliton solutions for novel truncated M-fractional Cahn–Allen (t-MfCA) models to secure different soliton solutions via the unified scheme. This model has significant in the area of mathematical physics and also known as reaction–diffusion. The obtained solutions are expressed in turns of trigonometric, hyperbolic and rational function solution under the condition on the free constraints. This work offers the kink, singular soliton, different type interaction of kink and lump wave for the numerical value of the free constraints. Form the obtained solution it is shown that the implement method is more informal, effective and reliable as compared to other methods. The calculation and all analytic solutions are verified by computational software MAPLE 18.},
     year = {2022}
    }
    

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  • TY  - JOUR
    T1  - Novel Exact Soliton Solutions of Cahn–Allen Models with Truncated M-fractional Derivative
    AU  - Mohammad Mobarak Hossain
    AU  - Md. Mamunur Roshid
    AU  - Md. Abu Naim Sheikh
    AU  - Mohammad Abu Taher
    AU  - Harun-Or-Roshid
    Y1  - 2022/12/29
    PY  - 2022
    N1  - https://doi.org/10.11648/j.ijtam.20220806.11
    DO  - 10.11648/j.ijtam.20220806.11
    T2  - International Journal of Theoretical and Applied Mathematics
    JF  - International Journal of Theoretical and Applied Mathematics
    JO  - International Journal of Theoretical and Applied Mathematics
    SP  - 112
    EP  - 120
    PB  - Science Publishing Group
    SN  - 2575-5080
    UR  - https://doi.org/10.11648/j.ijtam.20220806.11
    AB  - In recent research the effect of different type fractional derivative to nonlinear evolution equations plays a vital rule in the various branches of science and engineering. The nonlinear physical phenomena are expressed by nonlinear partial differential equations which are characteristics on the field of solid-state physics, plasma physics, fluid mechanics, chemical physics, mechanics, biology, chemistry, and so on. To visualize and identify their properties, it is essential to find the exact and multi solitons of the related nonlinear partial differential equation. In this work, we investigate more soliton solutions for novel truncated M-fractional Cahn–Allen (t-MfCA) models to secure different soliton solutions via the unified scheme. This model has significant in the area of mathematical physics and also known as reaction–diffusion. The obtained solutions are expressed in turns of trigonometric, hyperbolic and rational function solution under the condition on the free constraints. This work offers the kink, singular soliton, different type interaction of kink and lump wave for the numerical value of the free constraints. Form the obtained solution it is shown that the implement method is more informal, effective and reliable as compared to other methods. The calculation and all analytic solutions are verified by computational software MAPLE 18.
    VL  - 8
    IS  - 6
    ER  - 

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Author Information
  • Department of Mathematics, Hamdard University Bangladesh, Gazaria, Munshiganj, Bangladesh

  • Department of Mathematics, Hamdard University Bangladesh, Gazaria, Munshiganj, Bangladesh

  • Department of Mathematics, Dhaka University of Engineering and Technology (DUET), Gazipur, Bangladesh

  • Department of Mathematics, Dhaka University of Engineering and Technology (DUET), Gazipur, Bangladesh

  • Department of Mathematics, Pabna University of Science and Technology, Pabna, Bangladesh

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