New exact solitary wave solutions for fractional model

Ayyaz Ali; Zafar Ullah; Irfan Waheed; Moin-ud-Din Junjua; Muhammad Mohsen Saleem; Gulnaz Atta; Maimoona Karim; Ather Qayyum; Ayyaz Ali; Zafar Ullah; Irfan Waheed; Moin-ud-Din Junjua; Muhammad Mohsen Saleem; Gulnaz Atta; Maimoona Karim; Ather Qayyum

doi:10.3934/math.20221022

AIMS Mathematics

2022, Volume 7, Issue 10: 18587-18602. doi: 10.3934/math.20221022

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Research article Special Issues

New exact solitary wave solutions for fractional model

1.
Department of Mathematics, Institute of Southern Punjab Multan-Pakistan
2.
Department of Mathematics, Division of Science and Technology, University of Education Lahore, Pakistan
3.
Department of Mathematics, Department of Mathematics Ghazi University Dera Ghazi Khan Pakistan
4.
Department of Mathematics, University of Faisalabad-Pakistan

Received: 28 March 2022 Revised: 21 July 2022 Accepted: 28 July 2022 Published: 19 August 2022
MSC : 35C08, 34K20, 32W50

This manuscript involves the new exact solitary wave solutions of fractional reaction-diffusion model using the exp $ \mathrm{(-\ }\varphi \left(\eta \right) \mathrm{)} $-expansion method. The spatial model of fractional form is applied in modeling super-diffusive systems in the field of engineering, biology, physics (neutron diffusion theory), ecology, finance, and chemistry. The findings of miscellaneous studies showed that presented method is efficient for exploring new exact solutions to solve the complexities arising in mathematical physics and applied sciences. The new solutions which are obtained in the form of the rational, exponential, hyperbolic and trigonometric functions have a wide range in physics and engineering fields. Several results would be obtained under various parameters which shows good agreement with the previous published results of different papers. The proposed method can be extended to solve further problems arising in the engineering fields. My main contribution is programming and comparisons.
- reaction-diffusion equation,
- exact solutions,
- $ (-\varphi \left(\eta \right)) $-expansion technique,
- exp Caputo's derivative
Citation: Ayyaz Ali, Zafar Ullah, Irfan Waheed, Moin-ud-Din Junjua, Muhammad Mohsen Saleem, Gulnaz Atta, Maimoona Karim, Ather Qayyum. New exact solitary wave solutions for fractional model[J]. AIMS Mathematics, 2022, 7(10): 18587-18602. doi: 10.3934/math.20221022

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Abstract

This manuscript involves the new exact solitary wave solutions of fractional reaction-diffusion model using the exp $ \mathrm{(-\ }\varphi \left(\eta \right) \mathrm{)} $-expansion method. The spatial model of fractional form is applied in modeling super-diffusive systems in the field of engineering, biology, physics (neutron diffusion theory), ecology, finance, and chemistry. The findings of miscellaneous studies showed that presented method is efficient for exploring new exact solutions to solve the complexities arising in mathematical physics and applied sciences. The new solutions which are obtained in the form of the rational, exponential, hyperbolic and trigonometric functions have a wide range in physics and engineering fields. Several results would be obtained under various parameters which shows good agreement with the previous published results of different papers. The proposed method can be extended to solve further problems arising in the engineering fields. My main contribution is programming and comparisons.

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