A Comparative Analysis of Fractional-Order Kaup–Kupershmidt Equation within Different Operators

Shah, Nehad Ali; Hamed, Y. S.; Abualnaja, Khadijah M.; Chung, Jae Dong; Shah, Rasool; Khan, Adnan

doi:10.3390/sym14050986

Cited by 66 publications

(35 citation statements)

References 36 publications

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“…This method produces a solution in the form of a quick convergence series, which can be exact or approximate. Many physical phenomena which are modeled by fractional PDEs are solved by using NTDM [62][63][64].…”

Section: Introductionmentioning

confidence: 99%

Fractional View Analysis of Kuramoto–Sivashinsky Equations with Non-Singular Kernel Operators

et al. 2022

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In this article, we investigate the nonlinear model describing the various physical and chemical phenomena named the Kuramoto–Sivashinsky equation. We implemented the natural decomposition method, a novel technique, mixed with the Caputo–Fabrizio (CF) and Atangana–Baleanu deriavatives in Caputo manner (ABC) fractional derivatives for obtaining the approximate analytical solution of the fractional Kuramoto–Sivashinsky equation (FKS). The proposed method gives a series form solution which converges quickly towards the exact solution. To show the accuracy of the proposed method, we examine three different cases. We presented proposed method results by means of graphs and tables to ensure proposed method validity. Further, the behavior of the achieved results for the fractional order is also presented. The results we obtain by implementing the proposed method shows that our technique is extremely efficient and simple to investigate the behaviour of nonlinear models found in science and technology.

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Section: Introductionmentioning

confidence: 99%

Fractional View Analysis of Kuramoto–Sivashinsky Equations with Non-Singular Kernel Operators

et al. 2022

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“…As a result of the invention of fractional calculus, it was discovered that FDEs have more real-world applications than ODEs [10,11]. FDEs in fractional calculus are widely used in many mathematical and scientific fields, including bioengineering, blood circulation phenomena, aircraft design, viscoelasticity, electronic systems, electro-analytical chemistry, neuroscience, control theory, finance, hydrogeology, and control mechanisms [12][13][14][15][16][17]. Symmetry analysis is beautiful, especially when it comes to the study of partial differential equations and, more specifically, those equations that come from the mathematics of finance.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of the Fractional Coupled Burgers and Hirota–Satsuma KdV Equations via Analytical Techniques

Yasmin

Iqbal

2022

Symmetry

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This paper applies modified analytical methods to the fractional-order analysis of one and two-dimensional nonlinear systems of coupled Burgers and Hirota–Satsuma KdV equations. The Atangana–Baleanu fractional derivative operator and the Elzaki transform will be used to solve the proposed problems. The results of utilizing the proposed techniques are compared to the exact solution. The technique’s convergence is successfully presented and mathematically proven. To demonstrate the efficacy of the suggested techniques, we compared actual and analytic solutions using figures, which are in strong agreement with one another. Furthermore, the solutions achieved by applying the current techniques at different fractional orders are compared to the integer order. The proposed methods are appealing, simple, and accurate, indicating that they are appropriate for solving partial differential equations or systems of partial differential equations.

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“…Several integral transforms are developed, such as: the Sumudu transform, Elzaki transform, Natural transform, Pourreza transform, G-transform, Sawi transform, Shehu transform, and others [1][2][3][4][5][6][7][8][9]. These transforms provided in the literature are applied to solve several integral equations, ODEs, PDEs, and fractional PDEs [10][11][12][13][14][15][16][17]. Fusion of these transforms with semi-analytical techniques such as ADM, DTM, HPM, and VIM can also create novel and efficient regimes to solve such equations [18][19][20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions

2022

Self Cite

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In the present research paper, an iterative approach named the iterative Shehu transform method is implemented to solve time-fractional hyperbolic telegraph equations in one, two, and three dimensions, respectively. These equations are the prominent ones in the field of physics and in some other significant problems. The efficacy and authenticity of the proposed method are tested using a comparison of approximated and exact results in graphical form. Both 2D and 3D plots are provided to affirm the compatibility of approximated-exact results. The iterative Shehu transform method is a reliable and efficient tool to provide approximated and exact results to a vast class of ODEs, PDEs, and fractional PDEs in a simplified way, without any discretization or linearization, and is free of errors. A convergence analysis is also provided in this research.

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A Comparative Analysis of Fractional-Order Kaup–Kupershmidt Equation within Different Operators

Cited by 66 publications

References 36 publications

Fractional View Analysis of Kuramoto–Sivashinsky Equations with Non-Singular Kernel Operators

Fractional View Analysis of Kuramoto–Sivashinsky Equations with Non-Singular Kernel Operators

A Comparative Study of the Fractional Coupled Burgers and Hirota–Satsuma KdV Equations via Analytical Techniques

An Analytical Approach for Fractional Hyperbolic Telegraph Equation Using Shehu Transform in One, Two and Three Dimensions

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