A novel approach is proposed for obtaining exact travelling wave solutions to the space-time fractional Phi-4 equation

Ikram Ullah; Muhammad Bilal; Aditi Sharma; Hasim Khan; Shivam Bhardwaj; Sunil Kumar Sharma; Ikram Ullah; Muhammad Bilal; Aditi Sharma; Hasim Khan; Shivam Bhardwaj; Sunil Kumar Sharma

doi:10.3934/math.20241564

AIMS Mathematics

2024, Volume 9, Issue 11: 32674-32695. doi: 10.3934/math.20241564

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Research article

A novel approach is proposed for obtaining exact travelling wave solutions to the space-time fractional Phi-4 equation

1.
School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
2.
Department of Computer Science and Engineering, Symbiosis Institute of Technology, Symbiosis International (Deemed University), Pune, India
3.
Department of Mathematics, College of Science, Jazan University, P. O. Box 114, Jazan 45142, Saudi Arabia
4.
Mccombs School of Business, University of Texas at Austin, USA
5.
Department of Information Systems College of Computer and Information Sciences Majmaah University, Majmaah 11952, Saudi Arabia

Received: 12 September 2024 Revised: 22 October 2024 Accepted: 08 November 2024 Published: 19 November 2024
MSC : 65F10, 65H10, 90C30, 90C33

Complex physical occurrences currently need the use of nonlinear fractional partial differential equations. This paper provides a new approach to using the conformable derivative of Atangana to achieve exact travelling wave solutions to the space time-fractional Phi-4 problem. Our method enables a more profound comprehension of complex mathematical physics processes. We validate the solutions and demonstrate the effectiveness of our approaches in solving difficult nonlinear problems in nuclear and particle physics. Singular solutions can be retrieved by using the proposed method on nonlinear partial differential equations (NFPDEs). Our results are shown using contour and three-dimensional charts, which demonstrate various soliton formations for varying parameter values in the nonlinear zone. This study contributes to our growing knowledge of optical soliton.
Citation: Ikram Ullah, Muhammad Bilal, Aditi Sharma, Hasim Khan, Shivam Bhardwaj, Sunil Kumar Sharma. A novel approach is proposed for obtaining exact travelling wave solutions to the space-time fractional Phi-4 equation[J]. AIMS Mathematics, 2024, 9(11): 32674-32695. doi: 10.3934/math.20241564

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Abstract

Complex physical occurrences currently need the use of nonlinear fractional partial differential equations. This paper provides a new approach to using the conformable derivative of Atangana to achieve exact travelling wave solutions to the space time-fractional Phi-4 problem. Our method enables a more profound comprehension of complex mathematical physics processes. We validate the solutions and demonstrate the effectiveness of our approaches in solving difficult nonlinear problems in nuclear and particle physics. Singular solutions can be retrieved by using the proposed method on nonlinear partial differential equations (NFPDEs). Our results are shown using contour and three-dimensional charts, which demonstrate various soliton formations for varying parameter values in the nonlinear zone. This study contributes to our growing knowledge of optical soliton.

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