On the application of $ G_\alpha $ integral transform to nonlinear dynamical models with non-integer order derivatives

Rahmatullah Ibrahim Nuruddeen; Yasir Akbar; Hwajoon Kim; Rahmatullah Ibrahim Nuruddeen; Yasir Akbar; Hwajoon Kim

doi:10.3934/math.2022984

AIMS Mathematics

2022, Volume 7, Issue 10: 17859-17878. doi: 10.3934/math.2022984

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On the application of $ G_\alpha $ integral transform to nonlinear dynamical models with non-integer order derivatives

1.
Department of Mathematics, Federal University Dutse, Jigawa State, Nigeria
2.
COMSATS University Islamabad, Islamabad, Pakistan
3.
Kyungdong University, Yangju, Korea

Received: 12 June 2022 Revised: 22 July 2022 Accepted: 27 July 2022 Published: 03 August 2022
MSC : 44A05, 47J35

The current study uses an essential and integrated form of Laplace-type integral transform coupled with the Adomian's approach to study nonlinear evolution equations endowed with non-integer derivatives. More so, of particular interest here is to demonstrate the application of this transform to a wider class of nonlinear problems. Three test models have been examined by the presented method, and their closed-form solutions have been reported iteratively. Lastly, the variational effect of the non-integer order derivatives on the evolution of these models has been studied via the two and three-dimensional depictions.
- integral transform method,
- dynamical models,
- evolution equations,
- non-integer derivatives
Citation: Rahmatullah Ibrahim Nuruddeen, Yasir Akbar, Hwajoon Kim. On the application of $ G_\alpha $ integral transform to nonlinear dynamical models with non-integer order derivatives[J]. AIMS Mathematics, 2022, 7(10): 17859-17878. doi: 10.3934/math.2022984

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Abstract

The current study uses an essential and integrated form of Laplace-type integral transform coupled with the Adomian's approach to study nonlinear evolution equations endowed with non-integer derivatives. More so, of particular interest here is to demonstrate the application of this transform to a wider class of nonlinear problems. Three test models have been examined by the presented method, and their closed-form solutions have been reported iteratively. Lastly, the variational effect of the non-integer order derivatives on the evolution of these models has been studied via the two and three-dimensional depictions.

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