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Search Results (6)

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Keywords = double Laplace–Sumudu transform

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17 pages, 297 KiB  
Article
A Note on the Application of the Double Sumudu–Generalized Laplace Decomposition Method and 1+1- and 2+1-Dimensional Time-Fractional Boussinesq Equations
by Hassan Eltayeb and Said Mesloub
Symmetry 2024, 16(6), 665; https://doi.org/10.3390/sym16060665 - 28 May 2024
Viewed by 831
Abstract
The current paper concentrates on discovering the exact solutions of the singular time-fractional Boussinesq equation and coupled time-fractional Boussinesq equation by presenting a new technique known as the double Sumudu–generalized Laplace and Adomian decomposition method. Here, two main theorems are addressed that are [...] Read more.
The current paper concentrates on discovering the exact solutions of the singular time-fractional Boussinesq equation and coupled time-fractional Boussinesq equation by presenting a new technique known as the double Sumudu–generalized Laplace and Adomian decomposition method. Here, two main theorems are addressed that are very useful in this work. Moreover, the mentioned method is effective in solving several problems. Some examples are presented to check the precision and symmetry of the technique. The outcomes show that the proposed technique is precise and gives better solutions as compared to existing methods in the literature. Full article
(This article belongs to the Special Issue Discussion of Properties and Applications of Integral Transform)
21 pages, 470 KiB  
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
Axioms 2024, 13(1), 44; https://doi.org/10.3390/axioms13010044 - 11 Jan 2024
Cited by 2 | Viewed by 1506
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 [...] Read more.
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). Full article
(This article belongs to the Special Issue Fractional Calculus - Theory and Applications II)
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20 pages, 317 KiB  
Article
Application of the Double Sumudu-Generalized Laplace Transform Decomposition Method to Solve Singular Pseudo-Hyperbolic Equations
by Hassan Eltayeb
Symmetry 2023, 15(9), 1706; https://doi.org/10.3390/sym15091706 - 6 Sep 2023
Cited by 1 | Viewed by 1256
Abstract
In this study, the technique established by the double Sumudu transform in combination with a new generalized Laplace transform decomposition method, which is called the double Sumudu-generalized Laplace transform decomposition method, is applied to solve general two-dimensional singular pseudo-hyperbolic equations subject to the [...] Read more.
In this study, the technique established by the double Sumudu transform in combination with a new generalized Laplace transform decomposition method, which is called the double Sumudu-generalized Laplace transform decomposition method, is applied to solve general two-dimensional singular pseudo-hyperbolic equations subject to the initial conditions. The applicability of the proposed method is analyzed through demonstrative examples. The results obtained show that the procedure is easy to carry out and precise when employed for different linear and non-linear partial differential equations. Full article
(This article belongs to the Special Issue Various Approaches for Generalized Integral Transforms)
15 pages, 285 KiB  
Article
Application of Double Sumudu-Generalized Laplace Decomposition Method for Solving 2+1-Pseudoparabolic Equation
by Hassan Eltayeb
Axioms 2023, 12(8), 799; https://doi.org/10.3390/axioms12080799 - 19 Aug 2023
Cited by 4 | Viewed by 1250
Abstract
The main purpose of this research paper is to discuss the solution of the singular two-dimensional pseudoparabolic equation by employing the double Sumudu-generalized Laplace transform decomposition method (DSGLTDM). We establish two theorems related to the partial derivatives. Furthermore, to investigate the relevance of [...] Read more.
The main purpose of this research paper is to discuss the solution of the singular two-dimensional pseudoparabolic equation by employing the double Sumudu-generalized Laplace transform decomposition method (DSGLTDM). We establish two theorems related to the partial derivatives. Furthermore, to investigate the relevance of the proposed method to solving singular two-dimensional pseudo parabolic equations, three examples are provided. Full article
(This article belongs to the Special Issue Recent Advances in Special Functions and Applications)
19 pages, 4892 KiB  
Article
Conformable Double Laplace–Sumudu Iterative Method
by Shams A. Ahmed, Ahmad Qazza, Rania Saadeh and Tarig M. Elzaki
Symmetry 2023, 15(1), 78; https://doi.org/10.3390/sym15010078 - 28 Dec 2022
Cited by 16 | Viewed by 1907
Abstract
This research introduces a novel approach that combines the conformable double Laplace–Sumudu transform (CDLST) and the iterative method to handle nonlinear partial problems considering some given conditions, and we call this new approach the conformable Laplace–Sumudu iterative (CDLSI) method. Furthermore, we state and [...] Read more.
This research introduces a novel approach that combines the conformable double Laplace–Sumudu transform (CDLST) and the iterative method to handle nonlinear partial problems considering some given conditions, and we call this new approach the conformable Laplace–Sumudu iterative (CDLSI) method. Furthermore, we state and discuss the main properties and the basic results related to the proposed technique. The new method provides approximate series solutions that converge to a closed form of the exact solution. The advantage of using this method is that it produces analytical series solutions for the target equations without requiring discretization, transformation, or restricted assumptions. Moreover, we present some numerical applications to defend our results. The results demonstrate the strength and efficiency of the presented method in solving various problems in the fields of physics and engineering in symmetry with other methods. Full article
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16 pages, 2635 KiB  
Article
Exact Solutions of Nonlinear Partial Differential Equations via the New Double Integral Transform Combined with Iterative Method
by Shams A. Ahmed, Ahmad Qazza and Rania Saadeh
Axioms 2022, 11(6), 247; https://doi.org/10.3390/axioms11060247 - 25 May 2022
Cited by 44 | Viewed by 4875
Abstract
This article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The solutions of nonlinear terms of these equations were [...] Read more.
This article demonstrates how the new Double Laplace–Sumudu transform (DLST) is successfully implemented in combination with the iterative method to obtain the exact solutions of nonlinear partial differential equations (NLPDEs) by considering specified conditions. The solutions of nonlinear terms of these equations were determined by using the successive iterative procedure. The proposed technique has the advantage of generating exact solutions, and it is easy to apply analytically on the given problems. In addition, the theorems handling the mode properties of the DLST have been proved. To prove the usability and effectiveness of this method, examples have been given. The results show that the presented method holds promise for solving other types of NLPDEs. Full article
(This article belongs to the Special Issue Calculus of Variations and Nonlinear Partial Differential Equations)
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