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 |
Cahn–Allen Models, Unified Scheme, Reaction–Diffusion
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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
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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Download@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}
}
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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