Strong interaction of Jafari decomposition method with nonlinear fractional-order partial differential equations arising in plasma via the singular and nonsingular kernels

Saima Rashid; Rehana Ashraf; Fahd Jarad; Saima Rashid; Rehana Ashraf; Fahd Jarad

doi:10.3934/math.2022444

AIMS Mathematics

2022, Volume 7, Issue 5: 7936-7963. doi: 10.3934/math.2022444

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Strong interaction of Jafari decomposition method with nonlinear fractional-order partial differential equations arising in plasma via the singular and nonsingular kernels

1.
Department of Mathematics, Government College University, Faisalabad, Pakistan
2.
Department of Mathematics, Lahore College Women University, 54000, Lahore, Pakistan
3.
Department of Mathematics, Çankaya University, Ankara, Turkey
4.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
5.
Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

Received: 17 October 2021 Revised: 29 January 2022 Accepted: 06 February 2022 Published: 22 February 2022
MSC : 46S40, 47H10, 54H25

This research utilizes the Jafari transform and the Adomian decomposition method to derive a fascinating explicit pattern for the outcomes of the KdV, mKdV, K(2,2) and K(3,3) models that involve the Caputo fractional derivative operator and the Atangana-Baleanu fractional derivative operator in the Caputo sense. The novel exact-approximate solutions are derived from the formulation of trigonometric, hyperbolic, and exponential function forms. Laser and plasma sciences may benefit from these solutions. It is demonstrated that this approach produces a simple and effective mathematical framework for tackling nonlinear problems. To provide additional context for these ideas, simulations are performed, employing a computationally packaged program to assist in comprehending the implications of solutions.
- Jafari transform,
- Adomian decomposition method,
- KdV and mKdV model,
- K(2,2) and K(3,3) equations
Citation: Saima Rashid, Rehana Ashraf, Fahd Jarad. Strong interaction of Jafari decomposition method with nonlinear fractional-order partial differential equations arising in plasma via the singular and nonsingular kernels[J]. AIMS Mathematics, 2022, 7(5): 7936-7963. doi: 10.3934/math.2022444

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Abstract

This research utilizes the Jafari transform and the Adomian decomposition method to derive a fascinating explicit pattern for the outcomes of the KdV, mKdV, K(2,2) and K(3,3) models that involve the Caputo fractional derivative operator and the Atangana-Baleanu fractional derivative operator in the Caputo sense. The novel exact-approximate solutions are derived from the formulation of trigonometric, hyperbolic, and exponential function forms. Laser and plasma sciences may benefit from these solutions. It is demonstrated that this approach produces a simple and effective mathematical framework for tackling nonlinear problems. To provide additional context for these ideas, simulations are performed, employing a computationally packaged program to assist in comprehending the implications of solutions.

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