Solution for fractional forced KdV equation using fractional natural decomposition method

P. Veeresha; D. G. Prakasha; Jagdev Singh; P. Veeresha; D. G. Prakasha; Jagdev Singh

doi:10.3934/math.2020054

AIMS Mathematics

2020, Volume 5, Issue 2: 798-810. doi: 10.3934/math.2020054

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Solution for fractional forced KdV equation using fractional natural decomposition method

1.
Department of Mathematics, Karnatak University, Dharwad-580003, Karnataka, India
2.
Department of Mathematics, Faculty of Science, Davangere University, Shivagangothri, Davangere-577007, Karnataka, India
3.
Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India

Received: 03 October 2019 Accepted: 10 December 2019 Published: 27 December 2019
MSC : 35Axx, 35Qxx, 35R11

The fractional natural decomposition method (FNDM) is employed in the present investigation to find the solution for fractional forced Korteweg-de Vries (FF-KdV) equation. Three distinct cases are chosen for each equation to validate and illustrate the effectiveness of the future technique. The behaviour for different values of Froude number (F_r) has been presented to assure the proficiency and reliability and of the considered method. Moreover, we captured the behaviour of the FNDM solution for distinct arbitrary order. The obtained results elucidate that, the considered method is very effective and easy to employ while analyse the behaviour of nonlinear fractional differential equations arising in connected areas of science and technology.
- forced KdV equation,
- fractional natural decomposition method,
- Caputo fractional derivative
Citation: P. Veeresha, D. G. Prakasha, Jagdev Singh. Solution for fractional forced KdV equation using fractional natural decomposition method[J]. AIMS Mathematics, 2020, 5(2): 798-810. doi: 10.3934/math.2020054

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Abstract

The fractional natural decomposition method (FNDM) is employed in the present investigation to find the solution for fractional forced Korteweg-de Vries (FF-KdV) equation. Three distinct cases are chosen for each equation to validate and illustrate the effectiveness of the future technique. The behaviour for different values of Froude number (F_r) has been presented to assure the proficiency and reliability and of the considered method. Moreover, we captured the behaviour of the FNDM solution for distinct arbitrary order. The obtained results elucidate that, the considered method is very effective and easy to employ while analyse the behaviour of nonlinear fractional differential equations arising in connected areas of science and technology.

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