A novel perspective to the local fractional Zakharov–Kuznetsov‐modified equal width dynamical model on Cantor sets

Wang, Kang‐Le

doi:10.1002/mma.8533

Cited by 10 publications

(8 citation statements)

References 26 publications

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“…Later, this proposed approach has also been examined in more than one spatial dimension, indicating that this method has a broader application in nonlinear PDE systems [22,23]. This study is particularly powerful for fractal theory and fractal calculus, and it can be seen as dependable in getting analytical solutions and suitable for other nonlinear issues [24][25][26].…”

Section: Introductionmentioning

confidence: 91%

A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order

Luo

Nadeem

Asjad

et al. 2022

Computational and Mathematical Methods in Medicine

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The purpose of this paper is to investigate the approximate solution of the casting-mould heterogeneous system with Caputo derivative under the homotopy idea. The symmetry design of the system contains the integer partial differential equations and the fractional-order partial differential equations. We apply Yang transform homotopy perturbation method ( Y T-HPM) to find the approximate solution of temperature distribution in the casting-mould heterogeneous system. The Y T-HPM is a combined form of Yang transform ( Y T) and the homotopy perturbation method (HPM) using He’s polynomials. Some examples are provided to demonstrate the superiority of the suggested technique. The significant findings reveal that Y T-HPM minimizes the enormous without imposing any assumptions. Due to its powerful and robust support for nonlinear problems, this approach presents a remarkable appearance in the functional studies of fractal calculus.

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Section: Introductionmentioning

confidence: 91%

A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order

Luo

Nadeem

Asjad

et al. 2022

Computational and Mathematical Methods in Medicine

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“…1641 2016) and so on Ghanbari and Abdon, 2020;Wang, 2022b). In recent years, as a new theory of fractional calculus, the local fractional calculus has been successfully used to explain many non-differentiable (ND) scientific problems, for instance, the shallow water surfaces (Yang et al, 2016), rheological (Yang et al, 2017a), physics (Wang et al, , 2023cYang, 2017;Wang, 2023c), circuits (Yang et al, 2017b;Zhao et al, 2017;Wang, 2023b;Banchuin, 2022;Banchuin, 2023;Wang et al, 2020), vibration and others. Inspired by the recent research results on fractal circuits, the purpose of this article is to derive a new I-order R-C zero state-response circuit (ZSRC) within the local fractional derivative (LFD).…”

Section: Local Fractional Calculusmentioning

confidence: 99%

On the zero state-response of the ℑ-order R-C circuit within the local fractional calculus

Wang

Liu

2023

COMPEL

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Purpose As a powerful mathematical analysis tool, the local fractional calculus has attracted wide attention in the field of fractal circuits. The purpose of this paper is to derive a new ℑ-order non-differentiable (ND) R-C zero state-response circuit (ZSRC) by using the local fractional derivative on the Cantor set for the first time. Design/methodology/approach A new ℑ-order ND R-C ZSRC within the local fractional derivative on the Cantor set is derived for the first time in this work. By defining the ND lumped elements via the local fractional derivative, the ℑ-order Kirchhoff voltage laws equation is established, and the corresponding solutions in the form of the Mittag-Leffler decay defined on the Cantor sets are derived by applying the local fractional Laplace transform and inverse local fractional Laplace transform. Findings The characteristics of the ℑ-order R-C ZSRC on the Cantor sets are analyzed and presented through the 2-D curves. It is found that the ℑ-order R-C ZSRC becomes the classic one when ℑ = 1. The comparative results between the ℑ-order R-C ZSRC and the classic one show that the proposed method is correct and effective and is expected to shed light on the theory study of the fractal electrical systems. Originality/value To the best of the authors’ knowledge, this paper, for the first time ever, proposes the ℑ-order ND R-C ZSRC within the local fractional derivative on the Cantor sets. The results of this paper are expected to give some new enlightenment to the development of the fractal circuits.

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“…It is well known that integer order derivatives are local in nature, so these derivatives do not accurately describe the problem, especially for processes with historical memory. Recently, the fractal and fractional derivatives have drawn wide attention, and has been used widely to describe many complex phenomenon arising in different fields such as the bioscience [6][7][8], optics [9,10], cold plasma [11], vibration [12][13][14], circuits [15,16], unsmooth boundary [17][18][19][20][21][22] and so on [23][24][25][26][27][28][29]. Due to the nonlocal and nonsingular properties of the fractional derivatives, the fractional derivatives are more suitable for modelling the complex processes with historical memory than integer derivatives.…”

Section: Introductionmentioning

confidence: 99%

Variational approach for the fractional exothermic reactions model with constant heat source in porous medium

Wang

2023

THERM SCI

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In this paper, a new fractional exothermic reactions model with constant heat source in porous media considering the memory effect is proposed. Applying the fractional complex transform, the fractional model is converted into its partner. Then the variational principle of the problem is successfully established. Based on the obtained variational principle, the Ritz method is used to seek the solution of the fractional model. Finally, the correctness and effectiveness of the proposed method are illustrated by the numerical results with the aid of the MATLAB. The obtained results show that the proposed method is easy but effective, and is expected to shed a bright light on practical applications of fractional calculus.

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A novel perspective to the local fractional Zakharov–Kuznetsov‐modified equal width dynamical model on Cantor sets

Cited by 10 publications

References 26 publications

A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order

A Computational Approach for the Calculation of Temperature Distribution in Casting-Mould Heterogeneous System with Fractional Order

On the zero state-response of the ℑ-order R-C circuit within the local fractional calculus

Variational approach for the fractional exothermic reactions model with constant heat source in porous medium

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