A new efficient technique using Laplace transforms and smooth expansions to construct a series solution to the time-fractional Navier-Stokes equations

Burqan, Aliaa; El-Ajou, Ahmad; Saadeh, Rania; Al‐Smadi, Mohammed

doi:10.1016/j.aej.2021.07.020

Cited by 59 publications

(32 citation statements)

References 49 publications

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“…It was widely used by Ramanujan as a tool in computing definite integrals and infinite series. The theorems presented in this article are just as powerful and efficient as Ramanujan's master theorem in solving some families of improper integrals, for more about integral transforms, see [5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

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New Theorems in Solving Families of Improper Integrals

Abu-Ghuwaleh

Saadeh

Burqan

2022

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Many improper integrals appear in the classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik. It is a challenge for some researchers to determine the method in which these integrations are formed or solved. In this article, we present some new theorems to solve different families of improper integrals. In addition, we establish new formulas of integrations that cannot be solved by mathematical software such as Mathematica or Maple. In this article, we present three main theorems that are essential in generating new formulas for solving improper integrals. To show the efficiency and the simplicity of the presented techniques, we present some applications and examples on integrations that cannot be solved by regular methods. Furthermore, we acquire new results for integrations and compare them to that obtained in the classical table of integrations. Some previous results, become special cases of our outcomes or generalizations to acquire new integrals.

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Section: Introductionmentioning

confidence: 99%

“…In the history of mathematics, there are many improper integrals that appeared in the fields of science, physics, engineering and etc., [1][2][3][4][5]. Some of these integrals can be solved easily and others need some techniques to be solved.…”

Section: Introductionmentioning

confidence: 99%

New Theorems in Solving Families of Improper Integrals

Abu-Ghuwaleh

Saadeh

Burqan

2022

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“…The Laplace Residual power series method (LRPSM) [44][45][46] is a combination of the Laplace transform (LT) and RPSM [47][48][49][50][51][52]. In the LRPSM technique, the Laplace transform (LT) is used to simplify the focused problem into new algebraic equations.…”

Section: Introductionmentioning

confidence: 99%

A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas

et al. 2022

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In this paper, fractional-order system gas dynamics equations are solved analytically using an appealing novel method known as the Laplace residual power series technique, which is based on the coupling of the residual power series approach with the Laplace transform operator to develop analytical and approximate solutions in quick convergent series types by utilizing the idea of the limit with less effort and time than the residual power series method. The given model is tested and simulated to confirm the proposed technique’s simplicity, performance, and viability. The results show that the above-mentioned technique is simple, reliable, and appropriate for investigating nonlinear engineering and physical problems.

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“…In this regard, some recent techniques are proposed for solving FDEs. Among them decomposition technique, symmetric perturbation technique, variable frequency technique, and partial differential transformation technique [20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Nonlinear Fractional Gradient-Based System Using Fractional Power Series Method

Abu-Gdairi

2022

Int. J. Anal. Appl.

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This paper adapted a reliable treatment technique, called the fractional residual power series, to the fractional gradient-based system in solving a class of nonlinear programming model in Caputo’s sense. The gradient-based system has been constructed to transform the nonlinear programming problem with equality constraints to unconstrained optimization problem, and then the fractional residual power series method is implemented to obtain the essential behavior of underlying problem. The proposed methods have been applied effectively to produce optimal solution in rapidly convergent fractional series representations without linearization, or any limitations. To confirm the performance of the proposed methods, some optimization problems are tested. Further, numerical comparisons with other existing methods are also given. The results exhibit that the FRPS method is easy, simple, effective, and fully compatible with the complexity of such models.

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A new efficient technique using Laplace transforms and smooth expansions to construct a series solution to the time-fractional Navier-Stokes equations

Cited by 59 publications

References 49 publications

New Theorems in Solving Families of Improper Integrals

New Theorems in Solving Families of Improper Integrals

A Reliable Way to Deal with Fractional-Order Equations That Describe the Unsteady Flow of a Polytropic Gas

Analytical Solution of Nonlinear Fractional Gradient-Based System Using Fractional Power Series Method

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