Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel Transform

Nonlaopon, Kamsing; Alsharif, Abdullah M.; Zidan, Ahmed M.; Khan, Adnan; Hamed, Y. S.; Shah, Rasool

doi:10.3390/sym13071263

Cited by 71 publications

(32 citation statements)

References 42 publications

(35 reference statements)

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“…For the numerical result of many traditional order differential equations by applying other techniques, interested readers can refer to Refs. [20][21][22][23][24][25]. Numerous strategies have been used to study the solution to the given non-linear coupled scheme (1) of PDEs.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Time-Fractional Whitham-Broer-Kaup Equations with Exponential-Decay Kernel

Yasmin¹

2022

Fractal Fract

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This paper presents the semi-analytical analysis of the fractional-order non-linear coupled system of Whitham-Broer-Kaup equations. An iterative process is designed to analyze analytical findings to the specified non-linear partial fractional derivatives scheme utilizing the Yang transformation coupled with the Adomian technique. The fractional derivative is considered in the sense of Caputo-Fabrizio. Two numerical problems show the suggested method. Moreover, the results of the suggested technique are compared with the solution of other well-known numerical techniques such as the Homotopy perturbation technique, Adomian decomposition technique, and the Variation iteration technique. Numerical simulation has been carried out to verify that the suggested methodologies are accurate and reliable, and the results are revealed using graphs and tables. Comparing the analytical and actual solutions demonstrates that the proposed approaches effectively solve complicated non-linear problems. Furthermore, the proposed methodologies control and manipulate the achieved numerical solutions in a vast acceptable region in an extreme manner. It will provide us with a simple process to control and adjust the convergence region of the series solution.

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Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Time-Fractional Whitham-Broer-Kaup Equations with Exponential-Decay Kernel

Yasmin¹

2022

Fractal Fract

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“…In recent years, fractional partial differential equations (FPDEs) have gained considerable interest because of their applications in various fields such as finance, biological processes and systems, fluid flow [11,12], chaotic dynamics, electrochemistry, diffusion processes, material science, electromagnetic, turbulent flow [13][14][15][16][17][18], elastoplastic indentation problems [19], dynamics of van der Pol equation [20], and statistical mechanics model [21].…”

Section: Introductionmentioning

confidence: 99%

Fractional Analysis of Coupled Burgers Equations within Yang Caputo-Fabrizio Operator

Shah

El‐Zahar

Chung

2022

Journal of Function Spaces

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This work applies a novel analytical technique to the fractional view analysis of coupled Burgers equations. The proposed problems have been fractionally analyzed in the Caputo-Fabrizio sense. The Yang transformation was initially applied to the specified problem in the current approach. The series form solution is then obtained using the Adomian decomposition technique. The desired analytical solution is obtained after performing the inverse transform. Specific examples of fractional Burgers couple systems are used to validate the proposed technique. The current strategy has been found to be a useful methodology with a close match to actual solutions. The proposed method offers a lower computing cost and a faster convergence rate. As a result, the suggested technique can be applied to a variety of fractional order problems.

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“…ese mathematical phenomena enable a more accurate description of an actual object than using "integer" methods [7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

Analytical Investigation of Noyes–Field Model for Time‐Fractional Belousov–Zhabotinsky Reaction

et al. 2021

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In this article, we find the solution of time-fractional Belousov–Zhabotinskii reaction by implementing two well-known analytical techniques. The proposed methods are the modified form of the Adomian decomposition method and homotopy perturbation method with Yang transform. In Caputo manner, the fractional derivative is used. The solution we obtained is in the form of series which helps in investigating the analytical solution of the time-fractional Belousov–Zhabotinskii (B-Z) system. To verify the accuracy of the proposed methods, an illustrative example is taken, and through graphs, the solution is shown. Also, the fractional-order and integer-order solutions are compared with the help of graphs which are easy to understand. It has been verified that the solution obtained by using the given approaches has the desired rate of convergence to the exact solution. The proposed technique’s principal benefit is the low amount of calculations required. It can also be used to solve fractional-order physical problems in a variety of domains.

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Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel Transform

Cited by 71 publications

References 42 publications

Numerical Analysis of Time-Fractional Whitham-Broer-Kaup Equations with Exponential-Decay Kernel

Numerical Analysis of Time-Fractional Whitham-Broer-Kaup Equations with Exponential-Decay Kernel

Fractional Analysis of Coupled Burgers Equations within Yang Caputo-Fabrizio Operator

Analytical Investigation of Noyes–Field Model for Time‐Fractional Belousov–Zhabotinsky Reaction

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