The Caputo–Fabrizio time-fractional Sharma–Tasso–Olver–Burgers equation and its valid approximations

Hosseini, K.; Ilie, Mousa; Mirzazadeh, Mohammad; Băleanu, Dumitru; Park, Choonkil; Salahshour, Soheil

doi:10.1088/1572-9494/ac633e

Cited by 9 publications

(2 citation statements)

References 35 publications

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“…Caputo-Fabrizio derivative has been successfully used in the study of general form of Walter’s-B fluid model [ 14 ], a new dynamical model of hepatitis E [ 15 ], a new fractional differential model for COVID-19 transmission [ 16 ], mathematical modeling of human liver [ 17 ] and others. The Caputo-Fabrizio derivative has been used to solve fractional Sharma-Tasso-Olver-Burgers equation and (2+ 1)-dimensional mKdV equation [ 18 , 19 ].…”

Section: Introductionmentioning

confidence: 99%

Solution of time-fractional gas dynamics equation using Elzaki decomposition method with Caputo-Fabrizio fractional derivative

Sadaf,

Perveen,

Akram

et al. 2024

PLoS ONE

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In this article, Elzaki decomposition method (EDM) has been applied to approximate the analytical solution of the time-fractional gas-dynamics equation. The time-fractional derivative is used in the Caputo-Fabrizio sense. The proposed method is implemented on homogenous and non-homogenous cases of the time-fractional gas-dynamics equation. A comparison between the exact and approximate solutions is also provided to show the validity and accuracy of the technique. A graphical representation of all the retrieved solutions is shown for different values of the fractional parameter. The time development of all solutions is also represented in 2D graphs. The obtained results may help understand the physical systems governed by the gas-dynamics equation.

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Section: Introductionmentioning

confidence: 99%

Solution of time-fractional gas dynamics equation using Elzaki decomposition method with Caputo-Fabrizio fractional derivative

Sadaf,

Perveen,

Akram

et al. 2024

PLoS ONE

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“…In 2014, Hussan and Abbas 7 applied the Newton-Kantorovich method to solve a diffusion and exothermic equation, they applied the Newton-Kantorovich method to convert the non-linear boundary value problem into a linear boundary value problem, and then they used the finite difference method to solve the linear boundary value problem. There are different methods to handle non-linear differential equations, some of the most recent of them included in the references [8][9][10][11] . In this paper, the same procedure included in the work of Hussan and Abbas 7 is followed.…”

Section: Introductionmentioning

confidence: 99%

Newton-Kantorovich Method for Solving One of the Non-Linear Sturm-Liouville Problems

2023

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Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’ knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by applying the well-known Newton-Kantorovich method. Also, to show the efficiency of applying this method to solve these problems, a comparison is made in this paper between the Newton-Kantorovich method and the Adomian decomposition method applied to the same non-linear Sturm-Liouville problems under consideration in this work. As a result of this comparison, the results of the Newton-Kantorovich method agreed with the results obtained by applying Adomian’s decomposition method.

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Sensitivity and wave propagation analysis of the time-fractional (3+1)-dimensional shallow water waves model

Şenol,

Gençyiğit,

Demirbilek

et al. 2024

Z. Angew. Math. Phys.

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This study investigates the exact solutions of the time-fractional (3+1)-dimensional combined Korteweg–de Vries Benjamin–Bona–Mahony (KdV-BBM) equation. The considered model describes the long surface gravity waves of small amplitude, which portrays the two-way propagation of waves. The modified generalized Kudryashov method and the exp(-$$\varphi (\xi $$ φ ( ξ ))-expansion methods are employed to resolve the aforementioned issue because of their effectiveness and simplicity. For generality, the time fractional version is studied; more advanced solutions that do not exist in the literature were obtained. As a result, a variety of the exact wave solutions of the conformable (3+1)-dimensional KdV-BBM equation are obtained. The dynamical behaviors of some obtained solutions are represented with the proper parameter values. The used methods yield noteworthy results in obtaining the analytical solutions of fractional differential equations under various conditions. Besides, the sensitivity of regarding dynamical system is assessed to show the numerical stability effects.

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The Caputo–Fabrizio time-fractional Sharma–Tasso–Olver–Burgers equation and its valid approximations

Cited by 9 publications

References 35 publications

Solution of time-fractional gas dynamics equation using Elzaki decomposition method with Caputo-Fabrizio fractional derivative

Solution of time-fractional gas dynamics equation using Elzaki decomposition method with Caputo-Fabrizio fractional derivative

Newton-Kantorovich Method for Solving One of the Non-Linear Sturm-Liouville Problems

Sensitivity and wave propagation analysis of the time-fractional (3+1)-dimensional shallow water waves model

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