The analytical analysis of nonlinear fractional-order dynamical models

Xu, Jing; Khan, Hassan; Shah, Rasool; Alderremy, A. A.; Aly, Shaban; Băleanu, Dumitru

doi:10.3934/math.2021364

Cited by 13 publications

(4 citation statements)

References 35 publications

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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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“…Many researchers have been working on various aspects of fractional derivatives in recent years. Caputo and Fabrizio modified the existing Caputo derivative to develop the Caputo-Fabrizio fractional derivative [1][2][3][4][5] based on a nonsingular kernel. Because of its advantages, numerous researchers utilized this operator to investigate various types of fractional-order partial differential equations [6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

A Comparative Analysis of the Fractional‐Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law

Aljahdaly

Akgül

Shah

et al. 2022

Journal of Mathematics

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This article applies efficient methods, namely, modified decomposition method and new iterative transformation method, to analyze a nonlinear system of Korteweg–de Vries equations with the Atangana–Baleanu fractional derivative. The nonlinear fractional coupled systems investigated in this current analysis are the system of Korteweg–de Vries and the modified system of Korteweg–de Vries equations applied as a model in nonlinear physical phenomena arising in chemistry, biology, physics, and applied sciences. Approximate analytical results are represented in the form of a series with straightforward components, and some aspects showed an appropriate dependence on the values of the fractional-order derivatives. The convergence and uniqueness analysis is carried out. To comprehend the analytical procedure of both methods, three test examples are provided for the analytical results of the time-fractional KdV equation. Additionally, the efficiency of the mentioned procedures and the reduction in calculations provide broader applicability. It is also illustrated that the findings of the current methodology are in close harmony with the exact solutions. The series result achieved applying this technique is proved to be accurate and reliable with minimal calculations. The numerical simulations for obtained solutions are discussed for different values of the fractional order.

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“…Adomian decomposition method and Yang transform are two well-known techniques that have been applied to have introduced Yang decomposition method. Several physical phenomena which are modeled by partial differential equations and fractional partial differential equations are solved by applying Adomian transform decomposition method, such as the analytical investigation of fractional system partial differential equations are proposed in [29][30][31], the analysis of nonlinear ordinary differential equations is successfully shown in [32], nonlinear partial differential equations [33][34][35], fractional unsteady flow of fractional telegraph equations [36], polytropic gas model [37], fractional Schrodinger equation [38], and Fokker-Plank equation [39][40][41].…”

Section: Introductionmentioning

confidence: 99%

The Analysis of Fractional‐Order Proportional Delay Physical Models via a Novel Transform

2022

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In this paper, we deal with an alternative analytical analysis of fractional-order partial differential equations with proportional delay, achieved by applying Yang decomposition method, where the fractional derivative is taken in Caputo sense. The suggested series results are discovered to quickly converge to an exact solution. The computation of three test problems of fractional-order with proportional delay partial differential equations was presented to confirm the validity and efficiency of suggested method. The system appears to be a very dependable, effective, and powerful method for solving a variety of physical problems that arise in engineering and science.

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The analytical analysis of nonlinear fractional-order dynamical models

Cited by 13 publications

References 35 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

A Comparative Analysis of the Fractional‐Order Coupled Korteweg–De Vries Equations with the Mittag–Leffler Law

The Analysis of Fractional‐Order Proportional Delay Physical Models via a Novel Transform

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