A hybrid analytical technique for solving multi-dimensional time-fractional Navier-Stokes system

Emad Salah; Ahmad Qazza; Rania Saadeh; Ahmad El-Ajou; Emad Salah; Ahmad Qazza; Rania Saadeh; Ahmad El-Ajou

doi:10.3934/math.2023088

AIMS Mathematics

2023, Volume 8, Issue 1: 1713-1736. doi: 10.3934/math.2023088

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A hybrid analytical technique for solving multi-dimensional time-fractional Navier-Stokes system

1.
Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
2.
Department of Mathematics, Faculty of Science, Al Balqa Applied University, Salt 19117, Jordan

Received: 16 August 2022 Revised: 20 September 2022 Accepted: 28 September 2022 Published: 24 October 2022
MSC : 26A33, 35C10, 35R11, 44A10

In this research, a hybrid method, entitled the Laplace Residual Power Series technique, is adapted to find series solutions to a time-fractional model of Navier-Stokes equations in the sense of Caputo derivative. We employ the proposed method to construct analytical solutions to the target problem using the idea of the Laplace transform and the residual function with the concept of limit at infinity. A simple modification of the suggested method is presented to deal easily with the nonlinear terms constructed on the properties of the power series. Three interesting examples are solved and compared with the exact solutions to test the reliability, simplicity, and capacity of the presented method of solving systems of fractional partial differential equations. The results indicate that the used technique is a simple approach for solving nonlinear fractional differential equations since it depends only on the residual functions and the concept of the limit at infinity without needing differentiation or other complex computations.
- Caputo-fractional derivative,
- Laplace transform,
- series solutions,
- Navier-Stokes system
Citation: Emad Salah, Ahmad Qazza, Rania Saadeh, Ahmad El-Ajou. A hybrid analytical technique for solving multi-dimensional time-fractional Navier-Stokes system[J]. AIMS Mathematics, 2023, 8(1): 1713-1736. doi: 10.3934/math.2023088

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Abstract

In this research, a hybrid method, entitled the Laplace Residual Power Series technique, is adapted to find series solutions to a time-fractional model of Navier-Stokes equations in the sense of Caputo derivative. We employ the proposed method to construct analytical solutions to the target problem using the idea of the Laplace transform and the residual function with the concept of limit at infinity. A simple modification of the suggested method is presented to deal easily with the nonlinear terms constructed on the properties of the power series. Three interesting examples are solved and compared with the exact solutions to test the reliability, simplicity, and capacity of the presented method of solving systems of fractional partial differential equations. The results indicate that the used technique is a simple approach for solving nonlinear fractional differential equations since it depends only on the residual functions and the concept of the limit at infinity without needing differentiation or other complex computations.

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