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Volume 13
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Article

A Note on the Time-Fractional Navier–Stokes Equation and the Double Sumudu-Generalized Laplace Transform Decomposition Method

by
Hassan Eltayeb
*,
Imed Bachar
and
Said Mesloub
Mathematics Department, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi Arabia
*
Author to whom correspondence should be addressed.
Axioms 2024, 13(1), 44; https://doi.org/10.3390/axioms13010044
Submission received: 10 December 2023 / Revised: 26 December 2023 / Accepted: 9 January 2024 / Published: 11 January 2024
(This article belongs to the Special Issue Fractional Calculus - Theory and Applications II)
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Abstract

In this work, the time-fractional Navier–Stokes equation is discussed using a calculational method, which is called the Sumudu-generalized Laplace transform decomposition method (DGLTDM). The fractional derivatives are defined in the Caputo sense. The (DGLTDM) is a hybrid of the Sumudu-generalized Laplace transform and the decomposition method. Three examples of the time-fractional Navier–Stokes equation are studied to check the validity and demonstrate the effectiveness of the current method. The results show that the suggested method succeeds remarkably well in terms of proficiency and can be utilized to study more problems in the field of nonlinear fractional differential equations (FDEs).
Keywords: double Sumudu transform; double Sumudu-generalized Laplace transform; inverse double Sumudu-generalized Laplace transform; fractional Navier–Stokes equation; decomposition methods double Sumudu transform; double Sumudu-generalized Laplace transform; inverse double Sumudu-generalized Laplace transform; fractional Navier–Stokes equation; decomposition methods

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MDPI and ACS Style

Eltayeb, H.; Bachar, I.; Mesloub, S. A Note on the Time-Fractional Navier–Stokes Equation and the Double Sumudu-Generalized Laplace Transform Decomposition Method. Axioms 2024, 13, 44. https://doi.org/10.3390/axioms13010044

AMA Style

Eltayeb H, Bachar I, Mesloub S. A Note on the Time-Fractional Navier–Stokes Equation and the Double Sumudu-Generalized Laplace Transform Decomposition Method. Axioms. 2024; 13(1):44. https://doi.org/10.3390/axioms13010044

Chicago/Turabian Style

Eltayeb, Hassan, Imed Bachar, and Said Mesloub. 2024. "A Note on the Time-Fractional Navier–Stokes Equation and the Double Sumudu-Generalized Laplace Transform Decomposition Method" Axioms 13, no. 1: 44. https://doi.org/10.3390/axioms13010044

APA Style

Eltayeb, H., Bachar, I., & Mesloub, S. (2024). A Note on the Time-Fractional Navier–Stokes Equation and the Double Sumudu-Generalized Laplace Transform Decomposition Method. Axioms, 13(1), 44. https://doi.org/10.3390/axioms13010044

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