Fundamental solutions for the conformable time fractional Phi-4 and space-time fractional simplified MCH equations

Mahmoud A. E. Abdelrahman; S. Z. Hassan; R. A. Alomair; D. M. Alsaleh; Mahmoud A. E. Abdelrahman; S. Z. Hassan; R. A. Alomair; D. M. Alsaleh

doi:10.3934/math.2021386

AIMS Mathematics

2021, Volume 6, Issue 6: 6555-6568. doi: 10.3934/math.2021386

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Research article

Fundamental solutions for the conformable time fractional Phi-4 and space-time fractional simplified MCH equations

1.
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
2.
Department of Mathematics, Faculty of Science, Mansoura University, 35516 Mansoura, Egypt
3.
Department of Mathematics, College of Science and Humanities, Jubail, Imam Abdulrahman Bin Faisal University, Saudi Arabia
4.
Department of Mathematics, College of Science, Dammam, Imam Abdulrahman Bin Faisal University, Saudi Arabia

Received: 10 March 2021 Accepted: 09 April 2021 Published: 15 April 2021
MSC : 26A33, 34A45, 35C05, 35Q80, 35R11

We construct new solitary structures for time fractional Phi-4 and space-time fractional simplified modified Camassa-Holm (MCH) equations, utilizing the unified solver technique. The time (space-time) fractional derivatives are defined via sense of the new conformable fractional derivative. The unified solver technique extract vital solutions in explicit way. The obtained solutions may be beneficial for explaining many complex phenomena arising in fluid mechanics, nuclear, plasma and particle physics. The unified solver method is a vital tool for handling further models arising in applied science and new physics. For detailed physical dynamical representation of our results, 3D and 2D profiles to some of the gained solutions are also illustrated using Matlab software.
- fractional Phi-4 equation,
- fractional MCH equation,
- unified solver method,
- solitons,
- conformable derivative,
- physical applications
Citation: Mahmoud A. E. Abdelrahman, S. Z. Hassan, R. A. Alomair, D. M. Alsaleh. Fundamental solutions for the conformable time fractional Phi-4 and space-time fractional simplified MCH equations[J]. AIMS Mathematics, 2021, 6(6): 6555-6568. doi: 10.3934/math.2021386

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Abstract

We construct new solitary structures for time fractional Phi-4 and space-time fractional simplified modified Camassa-Holm (MCH) equations, utilizing the unified solver technique. The time (space-time) fractional derivatives are defined via sense of the new conformable fractional derivative. The unified solver technique extract vital solutions in explicit way. The obtained solutions may be beneficial for explaining many complex phenomena arising in fluid mechanics, nuclear, plasma and particle physics. The unified solver method is a vital tool for handling further models arising in applied science and new physics. For detailed physical dynamical representation of our results, 3D and 2D profiles to some of the gained solutions are also illustrated using Matlab software.

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