Application of the fractional oscillator model to describe damped vibrations

Рехвиашвили, С. Ш.; Pskhu, A. V.; Agarwal, Praveen; Jain, Shilpi

doi:10.3906/fiz-1811-16

Cited by 66 publications

(30 citation statements)

References 14 publications

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“…The study of fractional calculus, which involves fractional derivatives and integrals, has allured the interest of many in the field of engineering and natural sciences due to its monumental applications such as found in biotechnology [1], chaos theory [2], electrodynamics [3], random walk [4], signal and image processing [5,6], nanotechnology [7], viscoelasticity [8], and other various fields [9][10][11][12][13][14][15][16][17][18]. We also refer the reader to [19][20][21][22][23][24][25][26] for some recent applications of fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

Akinyemi

Iyiola

2020

Adv Differ Equ

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This paper employs an efficient technique, namely q-homotopy analysis transform method, to study a nonlinear coupled system of equations with Caputo fractional-time derivative. The nonlinear fractional coupled systems studied in this present investigation are the generalized Hirota-Satsuma coupled with KdV, the coupled KdV, and the modified coupled KdV equations which are used as a model in nonlinear physical phenomena arising in biology, chemistry, physics, and engineering. The series solution obtained using this method is proved to be reliable and accurate with minimal computations. Several numerical comparisons are made with well-known analytical methods and the exact solutions when α = 1. It is evident from the results obtained that the proposed method outperformed other methods in handling the coupled systems considered in this paper. The effect of the fractional order on the problem considered is investigated, and the error estimate when compared with exact solution is presented.Here, we present some useful definitions, properties, and notations that will be used in this work. Definition 2.1 The Riemann-Liouville (R-L) fractional integral of order α (α ≥ 0) of a function Q(x, t) ∈ C m , m ≥ -1, is given as [29, 63-65] J α Q(x, t) = 1 Γ (α) t 0

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Section: Introductionmentioning

confidence: 99%

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

Akinyemi

Iyiola

2020

Adv Differ Equ

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“…Fractional calculus is widely used to model many real-life problems in various fields such as physics, engineering, biology, earth science, chemistry, finance, and so on [1][2][3][4][5][6][7][8]. The fractional calculus was introduced more than 300 years ago [9].…”

Section: Introductionmentioning

confidence: 99%

On the solution of two-dimensional fractional Black–Scholes equation for European put option

Prathumwan

Trachoo

2020

Adv Differ Equ

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The purpose of this paper was to investigate the dynamics of the option pricing in the market through the two-dimensional time fractional-order Black-Scholes equation for a European put option. The Liouville-Caputo derivative was used to improve the ordinary Black-Scholes equation. The analytic solution is a powerful tool for describing the behavior of the option price in the European style market. In this study, analytic solution is carried out by the Laplace homotopy perturbation method. Moreover, the obtained solution showed that the Laplace homotopy perturbation method was an efficient method for finding an analytic solution of two-dimensional fractional-order differential equation.

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“…The physical situation at the surface may be unsuitable for attaching a sensor, or the accuracy of a surface measurement may be seriously impaired by the presence of the sensor. Typical practical applications are the estimation of the heat flux and the temperature at the surface of the body under investigation, e.g., re-entry vehicles, calorimeter-type instrumentation, and combustion chambers [1,2,5,11,13,15,16,19,20]. In such cases, one is restricted to interior measurements, and from these one wishes to compute the surface temperature.…”

Section: Introductionmentioning

confidence: 99%

A filter method for inverse nonlinear sideways heat equation

et al. 2020

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In this paper, we study a sideways heat equation with a nonlinear source in a bounded domain, in which the Cauchy data at x = X are given and the solution in 0 ≤ x < X is sought. The problem is severely ill-posed in the sense of Hadamard. Based on the fundamental solution to the sideways heat equation, we propose to solve this problem by the filter method of degree α, which generates a well-posed integral equation. Moreover, we show that its solution converges to the exact solution uniformly and strongly in L p (ω, X ; L 2 (R)), ω ∈ [0, X) under a priori assumptions on the exact solution. The proposed regularized method is illustrated by numerical results in the final section.

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Application of the fractional oscillator model to describe damped vibrations

Cited by 66 publications

References 14 publications

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

A reliable technique to study nonlinear time-fractional coupled Korteweg–de Vries equations

On the solution of two-dimensional fractional Black–Scholes equation for European put option

A filter method for inverse nonlinear sideways heat equation

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