Solving System of Conformable Fractional Differential Equations by Conformable Double Laplace Decomposition Method

Kayijuka, Idrissa

doi:10.4208/jpde.v33.n3.7

Cited by 7 publications

(2 citation statements)

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“…In the following figures, we sketch the 3D plot of the accurate solution of Equation (37) in Fig. 3 (a) which is the same approximate obtained solution, when putting η = γ = 1.…”

Section: Tablementioning

confidence: 78%

“…Numerous mathematicians and authors have created new methods to solve conformal differential problems, including the simplest method [26], Kudryashov method [27], double Shehu transform [28], Tanh method [29,30], reliable methods [31], double Sumudu transform [32,33], conformable Laplace transform (CLT) method [34,35], conformable double Laplace transform method [36], and conformable Sumudu transform (CST) method and others [37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

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Modified conformable double Laplace–Sumudu approach with applications

Ahmed

Saadeh

Qazza

et al. 2023

Heliyon

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“…In the following figures, we sketch the 3D plot of the accurate solution of Equation (37) in Fig. 3 (a) which is the same approximate obtained solution, when putting η = γ = 1.…”

Section: Tablementioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Modified conformable double Laplace–Sumudu approach with applications

Ahmed

Saadeh

Qazza

et al. 2023

Heliyon

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Analytical Solutions to Two-Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method

Deresse

2022

Advances in Mathematical Physics

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The conformable fractional triple Laplace transform approach, in conjunction with the new Iterative method, is used to examine the exact analytical solutions of the (2 + 1)-dimensional nonlinear conformable fractional Telegraph equation. All the fractional derivatives are in a conformable sense. Some basic properties and theorems for conformable triple Laplace transform are presented and proved. The linear part of the considered problem is solved using the conformable fractional triple Laplace transform method, while the noise terms of the nonlinear part of the equation are removed using the novel Iterative method’s consecutive iteration procedure, and a single iteration yields the exact solution. As a result, the proposed method has the benefit of giving an exact solution that can be applied analytically to the presented issues. To confirm the performance, correctness, and efficiency of the provided technique, two test modeling problems from mathematical physics, nonlinear conformable fractional Telegraph equations, are used. According to the findings, the proposed method is being used to solve additional forms of nonlinear fractional partial differential equation systems. Moreover, the conformable fractional triple Laplace transform iterative method has a small computational size as compared to other methods.

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Conformable Double Laplace–Sumudu Iterative Method

et al. 2022

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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.

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Solving System of Conformable Fractional Differential Equations by Conformable Double Laplace Decomposition Method

Cited by 7 publications

References 0 publications

Modified conformable double Laplace–Sumudu approach with applications

Modified conformable double Laplace–Sumudu approach with applications

Analytical Solutions to Two-Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method

Conformable Double Laplace–Sumudu Iterative Method

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