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Diethelm, Kai; Ford, Neville J.; Freed, Alan D.

doi:10.1023/a:1016592219341

Cited by 1,778 publications

(270 citation statements)

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“…For numerically solving the set of fractional order differential equations Eq. 7, the predictorcorrector method [22] is used. This method is known as a reliable method for simulation of fractional order chaotic systems [23].…”

Section: Effect Of Fractionality Of Capacitors On Differences Betweenmentioning

confidence: 99%

The effect of fractionality nature in differences between computer simulation and experimental results of a chaotic circuit

Faraji

Tavazoei

2013

Open Physics

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Abstract:In practice, some differences are usually observed between computer simulation and experimental results of a chaotic circuit. In this paper, it is tried to obtain computer simulation results having more correlation with those obtained in practice by using more realistic models for chaotic circuits. This goal is achieved by considering the fractionality nature of electrical capacitors in the model of a chaotic circuit. PACS

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Section: Effect Of Fractionality Of Capacitors On Differences Betweenmentioning

confidence: 99%

The effect of fractionality nature in differences between computer simulation and experimental results of a chaotic circuit

Faraji

Tavazoei

2013

Open Physics

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“…The obtained fractional equations cannot be solved analytically so easily in many cases; therefore we seek for the numerical schemes used for solving fractional differential equations (FDEs). These methods include the Grünwald-Letnikov approximation [2], decomposition method [16][17][18][19], variational iteration method [20], the Adams-Bashforth-Moulton method [21], etc.…”

Section: Introductionmentioning

confidence: 99%

The Motion of a Bead Sliding on a Wire in Fractional Sense

et al. 2017

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In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form. We first introduce the classical Lagrangian from the system model under consideration and obtain the classical EulerLagrange equation of motion. As the second step, we generalize the classical Lagrangian to the fractional form and derive the fractional Euler-Lagrange equation in terms of the Caputo fractional derivatives. Finally, we provide numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on a discretization scheme using a Grünwald-Letnikov approximation for the fractional derivatives. Numerical simulations verify that the proposed approach is efficient and easy to implement.

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“…The finite difference method is the most classic method for fractional differential equation [12][13][14][15][16]. The recent works can see the references [17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…However, high order accuracy schemes are seldom derived by finite difference method. In general, extrapolation method is applied in order to obtain a high accuracy [10,16]. It is well-known that spectral methods are superior to finite different methods in many instances for partial differential equations [20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Pseudo-Spectral Method for Space Fractional Diffusion Equation

Huang¹,

Zheng²

2013

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This paper presents a numerical scheme for space fractional diffusion equations (SFDEs) based on pseudo-spectral method. In this approach, using the Guass-Lobatto nodes, the unknown function is approximated by orthogonal polynomials or interpolation polynomials. Then, by using pseudo-spectral method, the SFDE is reduced to a system of ordinary differential equations for time variable t. The high order Runge-Kutta scheme can be used to solve the system. So, a high order numerical scheme is derived. Numerical examples illustrate that the results obtained by this method agree well with the analytical solutions.

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Cited by 1,778 publications

References 0 publications

The effect of fractionality nature in differences between computer simulation and experimental results of a chaotic circuit

The effect of fractionality nature in differences between computer simulation and experimental results of a chaotic circuit

The Motion of a Bead Sliding on a Wire in Fractional Sense

Pseudo-Spectral Method for Space Fractional Diffusion Equation

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