Numerical simulation and analysis of fractional-order Phi-Four equation

Azzh Saad Alshehry; Humaira Yasmin; Rasool Shah; Roman Ullah; Asfandyar Khan; Azzh Saad Alshehry; Humaira Yasmin; Rasool Shah; Roman Ullah; Asfandyar Khan

doi:10.3934/math.20231390

AIMS Mathematics

2023, Volume 8, Issue 11: 27175-27199. doi: 10.3934/math.20231390

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Numerical simulation and analysis of fractional-order Phi-Four equation

1.
Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia
2.
Department of Basic Sciences, Preparatory Year Deanship, King Faisal University, Al-Ahsa, 31982, Saudi Arabia
3.
Department of Mathematics, Abdul Wali University Mardan 23200, Pakistan
4.
Department of General Studies, Higher Colleges of Technology, Dubai Women Campus, UAE

Received: 04 August 2023 Revised: 30 August 2023 Accepted: 03 September 2023 Published: 25 September 2023
MSC : 33B15, 34A34, 35A20, 35A22, 44A10

This paper introduces a novel numerical approach for tackling the nonlinear fractional Phi-four equation by employing the Homotopy perturbation method (HPM) and the Adomian decomposition method (ADM), augmented by the Shehu transform. These established techniques are adept at addressing nonlinear differential equations. The equation's complexity is reduced by applying the Shehu Transform, rendering it amenable to solutions via HPM and ADM. The efficacy of this approach is underscored by conclusive results, attesting to its proficiency in solving the equation. With extensive ramifications spanning physics and engineering domains like fluid dynamics, heat transfer, and mechanics, the proposed method emerges as a precise and efficient tool for resolving nonlinear fractional differential equations pervasive in scientific and engineering contexts. Its potential extends to analogous equations, warranting further investigation to unravel its complete capabilities.
- Shehu transform,
- Adomian decomposition method,
- homotopy perturbation method,
- fractional Phi-four equation,
- Caputo operator
Citation: Azzh Saad Alshehry, Humaira Yasmin, Rasool Shah, Roman Ullah, Asfandyar Khan. Numerical simulation and analysis of fractional-order Phi-Four equation[J]. AIMS Mathematics, 2023, 8(11): 27175-27199. doi: 10.3934/math.20231390

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Abstract

This paper introduces a novel numerical approach for tackling the nonlinear fractional Phi-four equation by employing the Homotopy perturbation method (HPM) and the Adomian decomposition method (ADM), augmented by the Shehu transform. These established techniques are adept at addressing nonlinear differential equations. The equation's complexity is reduced by applying the Shehu Transform, rendering it amenable to solutions via HPM and ADM. The efficacy of this approach is underscored by conclusive results, attesting to its proficiency in solving the equation. With extensive ramifications spanning physics and engineering domains like fluid dynamics, heat transfer, and mechanics, the proposed method emerges as a precise and efficient tool for resolving nonlinear fractional differential equations pervasive in scientific and engineering contexts. Its potential extends to analogous equations, warranting further investigation to unravel its complete capabilities.

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