Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method

Mohamed, Mohamed Z.; Yousif, Mohammed Omer; Hamza, Amjad E.

doi:10.1155/2022/4743234

Cited by 17 publications

(6 citation statements)

References 20 publications

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“…The DSET for some fundamental functions is summed up in Table 1 below. □ Lemma 4 (see [20,27]). The single ST of u −1þα E β; α ðμu β Þ; takes the form:…”

Section: Preliminariesmentioning

confidence: 95%

Solving Partial Differential Equations of Fractional Order by Using a Novel Double Integral Transform

Ahmed,

Elzaki,

Mohamed

2023

Mathematical Problems in Engineering

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In this work, the double Sumudu–Elzaki transform was used for solving fractional-partial differential equations (FPDEs) with starting and boundary conditions. We will use the fractional-order derivative (Caputo’s derivatives) idea. Theorems and facts that are crucial to the newly introduced transform are also discussed and illustrated. By using this newly designed integral transform and its properties, FPDEs can be reduced into algebraic equations. This strategy has the precise answer since it does not need any discrimination, transformation, or limited assumptions. Five further instances were given to support our conclusions. The results showed that the recommended strategy is superb, reliable, and efficient. It is also a simple method for solving specific problems in a number of applied scientific and technical fields.

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“…The DSET for some fundamental functions is summed up in Table 1 below. □ Lemma 4 (see [20,27]). The single ST of u −1þα E β; α ðμu β Þ; takes the form:…”

Section: Preliminariesmentioning

confidence: 95%

Solving Partial Differential Equations of Fractional Order by Using a Novel Double Integral Transform

Ahmed,

Elzaki,

Mohamed

2023

Mathematical Problems in Engineering

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“…For instance, Mohammed [17] used the Conformable double Sumudu transform in solving a scalar time-fractional coupled Burgers equation. Also, the authors [18] solved a nonlinear one-dimensional fractional Burgers' equations with the aid of the Elzaki transform and homotopy perturbation method. In [19], the authors developed a modified variational iteration Laplace transform method and compared with Laplace Adomian decomposition method in solving a one-dimensional time-fractional Burgers Equations.…”

Section: Applicationsmentioning

confidence: 99%

Solution of the Modified Time Fractional Coupled Burgers Equations Using Laplace Adomian Decompostion Method

Omame

Zaman

2023

Acta Mechanica Et Automatica

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In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and Atangana-Baleanu operators are implemented for the equations. Also, two different scenarios are examined for each fractional operator: when the initial conditions are u(x, y, 0) = sin(xy), v(x, y, 0) = sin(xy), and when they are u(x, y, 0) = e{−kxy}, v(x, y, 0) = e{−kxy}, where k, α are some positive constants. With the aid of computable Adomian polynomials, the solutions are obtained using Laplace Adomian decomposition method (LADM). The method does not need linearization, weak nonlinearity assumptions or perturbation theory. Simulations are also presented to support theoretical results, and the behaviour of the solutions under the three different fractional operators compared.

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“…Z. Mohamed. et al [10] combined the Elzaki transform method with the new homotopy perturbation method for the first time and solve initial value problems numerically and analytically, such as nonlinear fractional differential equations of various normal orders. They found that the initial conditions have a big impact on the equations result.…”

Section: Introductionmentioning

confidence: 99%

Solutions of fractional differential equations using power series method and Sumudu transform

Zhang

2023

Preprint

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An analytic function can be approximated by its corresponding power series. The advantage of the Sumudu transform is to turn differential equations into algebraic equations. Combining the power series method with the Sumudu transform, the approximation solutions of the fractional differential equations are studied. Several numerical examples show the better, efficient and high accurate results by utilizing the proposed approach. 2020 MSC: O175.11

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Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method

Cited by 17 publications

References 20 publications

Solving Partial Differential Equations of Fractional Order by Using a Novel Double Integral Transform

Solving Partial Differential Equations of Fractional Order by Using a Novel Double Integral Transform

Solution of the Modified Time Fractional Coupled Burgers Equations Using Laplace Adomian Decompostion Method

Solutions of fractional differential equations using power series method and Sumudu transform

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