Conformable Sumudu Transform of Space-Time Fractional Telegraph Equation

Hamza, Amjad E.; Mohamed, Mohamed Z.; Elmohmoud, Eltaib M. Abd; Magzoub, M.

doi:10.1155/2021/6682994

Cited by 9 publications

(8 citation statements)

References 18 publications

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“…The basic definitions and important results of both conformable fractional derivative and RDTM in the conformable fractional derivative sense are briefly discussed. After dealing with four distinct conformable fractional telegraph equations from mathematical physics problems, the outcomes of exemplary research by the proposed method gave us a series solution that converged very quickly to the exact solutions that we anticipated from previous numerical instances, as illustrated throughout the references [47,49,50,59,60]. Tables 1-3 and Figures 1, 2, 3, 4, 5, 6, 7, and 8 for each investigated example exhibit the eighthterm approximate solutions by the proposed method in comparison to exact solutions.…”

Section: Discussionmentioning

confidence: 86%

“…Example 1 (see [49,50]). Consider the conformable fractional space-time telegraph equation stated as…”

Section: Analytical Solution To Illustrativementioning

confidence: 99%

“…Plugging equations ( 50) and ( 51) into equation (49), for k = 0, 1, 2, ⋯, we obtain the following successive iterated values:…”

Section: Analytical Solution To Illustrativementioning

confidence: 99%

“…More recently, many researchers have given their attention to examining the solutions of conformable fractional telegraph equations using different methods. In 2021, [49] obtained accurate and convergent numerical solutions of linear space-time matching telegraph fractional equations employing a double conformable Sumudu matching transformation method. Moreover, the numerical model is equipped to explain the work, the accuracy of the work, and sobriety in its presentation method, and as a result, the proposed method shows an effective and convenient way to employ proven problems in science and engineering.…”

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confidence: 99%

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Analytical Solution of One-Dimensional Nonlinear Conformable Fractional Telegraph Equation by Reduced Differential Transform Method

Deresse

2022

Advances in Mathematical Physics

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In this paper, the reduced differential transform method (RDTM) is successfully implemented to obtain the analytical solution of the space-time conformable fractional telegraph equation subject to the appropriate initial conditions. The fractional-order derivative will be in the conformable (CFD) sense. Some properties which help us to solve the governing problem using the suggested approach are proven. The proposed method yields an approximate solution in the form of an infinite series that converges to a closed-form solution, which is in many cases the exact solution. This method has the advantage of producing an analytical solution by only using the appropriate initial conditions without requiring any discretization, transformation, or restrictive assumptions. Four test modeling problems from mathematical physics, conformable fractional telegraph equations in which we already knew their exact solution using other numerical methods, were taken to show the liability, accuracy, convergence, and efficiency of the proposed method, and the solution behavior of each illustrative example is presented using tabulated numerical values and two- and three-dimensional graphs. The results show that the RDTM gave solutions that coincide with the exact solutions and the numerical solutions that are available in the literature. Also, the obtained results reveal that the introduced method is easily applicable and it saves a lot of computational work in solving conformable fractional telegraph equations, and it may also find wide application in other complicated fractional partial differential equations that originate in the areas of engineering and science.

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Section: Discussionmentioning

confidence: 86%

“…Example 1 (see [49,50]). Consider the conformable fractional space-time telegraph equation stated as…”

Section: Analytical Solution To Illustrativementioning

confidence: 99%

“…Plugging equations ( 50) and ( 51) into equation (49), for k = 0, 1, 2, ⋯, we obtain the following successive iterated values:…”

Section: Analytical Solution To Illustrativementioning

confidence: 99%

mentioning

confidence: 99%

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Analytical Solution of One-Dimensional Nonlinear Conformable Fractional Telegraph Equation by Reduced Differential Transform Method

Deresse

2022

Advances in Mathematical Physics

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“…Therefore, as one of the crucial equations in different fields of sciences, many scholars have recently focused their efforts on investigating the solutions of conformable fractional telegraph equations using various methodologies. Using a double conformable Sumudu matching transfor-mation approach, [25] discovered accurate and convergent numerical solutions of linear space-time matching telegraph fractional equations in 2021. Using the cosine family of linear operators, Bouaouid et al [26] established the existence, uniqueness, and stability of the integral solution of a nonlocal telegraph equation in the conformable timefractional derivative (see [12,[27][28][29][30] for more related work on the solution of conformable telegraph equations).…”

Section: Introductionmentioning

confidence: 99%

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 Sumudu transformations an efficient approximation solutions to the fractional coupled Burger’s equation

Mohamed

Hamza

Sedeeg

2023

Ain Shams Engineering Journal

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Conformable Sumudu Transform of Space-Time Fractional Telegraph Equation

Cited by 9 publications

References 18 publications

Analytical Solution of One-Dimensional Nonlinear Conformable Fractional Telegraph Equation by Reduced Differential Transform Method

Analytical Solution of One-Dimensional Nonlinear Conformable Fractional Telegraph Equation by Reduced Differential Transform Method

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

Conformable double Sumudu transformations an efficient approximation solutions to the fractional coupled Burger’s equation

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