He’s homotopy perturbation method for solving time fractional Swift-Hohenberg equations

Ban, Tao; Run-qing, Cui

doi:10.2298/tsci1804601b

Cited by 23 publications

(20 citation statements)

References 24 publications

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“…For the snow ball problem, x 0 is the porous size. This issue solicits some articles on fractional differential equations, which can be solved approximately by the homotopy perturbation method [10,11], the variational iteration method [12], and others.…”

mentioning

confidence: 99%

Two-scale mathematics and fractional calculus for thermodynamics

2019

Therm sci

271

156

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A three dimensional problem can be approximated by either a two-dimensional or one-dimensional case, but some information will be lost. To reveal the lost information due to the lower dimensional approach, two-scale mathematics is needed. Generally one scale is established by usage where traditional calculus works, and the other scale is for revealing the lost information where the continuum assumption might be forbidden, and fractional calculus or fractal calculus has to be used. The two-scale transform can approximately convert the fractional calculus into its traditional partner, making the two-scale thermodynamics much promising.

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mentioning

confidence: 99%

Two-scale mathematics and fractional calculus for thermodynamics

2019

Therm sci

271

156

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“…The fractal diffusion-reaction equation can be also solved by the homotopy perturbation method, variational iteration method or Taylor series method [30][31][32][33][34][35][36][37][38][39]. This paper gives an ample evidence that the fractal variational approach to amperometric enzymatic reactions is not only simple, but also rigorous.…”

Section: Fractal Variational Principlementioning

confidence: 98%

Fractal diffusion-reaction model for a porous electrode

2021

THERM SCI

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Fractal modifications of Fick?s laws are discussed by taking into account the electrode?s porous structure, and a fractal derivative model for diffusion-reaction process in a thin film of an amperometric enzymatic reaction is established. Particular attention is paid to giving an intuitive grasp for its fractal variational principle and its solution procedure. Extremely fast or extremely slow diffusion process can be achieved by suitable control of the electrode?s surface morphology, a sponge-like surface leads to an extremely fast diffusion, while a lotus-leaf-like uneven surface predicts an extremely slow process. This paper sheds a bright light on an optimal design of an electrode?s surface morphology.

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“…To inspect this case, we proceed using the technology of the expanded frequency as mentioned in the above section. Consequently, we employ the two expansions (12) and (13) into equation (30). Equating the identical powers of q; to zero, we obtain the first two unknowns, in the expansion (12), has the layout y 0 ðx; tÞ ¼ AðxÞcosXt (31)…”

Section: The Fractional Derivativementioning

confidence: 99%

A periodic solution of the fractional sine-Gordon equation arising in architectural engineering

Shen

El‐Dib

2020

Journal of Low Frequency Noise, Vibration and Active Control

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Many nonlinear vibrations arising in the engineering of architecture include noise and uncertain properties, and this paper suggests a fractional model to elucidate the properties. The fractional sine-Gordon equation with the Riemann-Liouville fractional derivative is used as an example to solve its periodic solution by the homotopy perturbation method. The frequency-amplitude relationship is obtained, and the effect of the fractional derivative order on the vibration property is discussed. Additionally, the harmonic resonance is also discussed. This preliminary research can be further extended to real applications.

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He’s homotopy perturbation method for solving time fractional Swift-Hohenberg equations

Abstract: This paper find the most effective method to solve the time-fractional Swift-Hohenberg equation with cubicquintic non-linearity by combining the homotopy perturbation method and the fractional complex transform. The solution reveals some intermittent properties of thermal physics.

Cited by 23 publications

References 24 publications

Two-scale mathematics and fractional calculus for thermodynamics

Two-scale mathematics and fractional calculus for thermodynamics

Fractal diffusion-reaction model for a porous electrode

A periodic solution of the fractional sine-Gordon equation arising in architectural engineering

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