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Analysis on the time and frequency domain for the RC electric circuit of fractional order

100%
Guía M., Gómez F., Rosales J.
Open Physics
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2013
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vol. 11
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issue 10
1366-1371
EN
This paper provides an analysis in the time and frequency domain of an RC electrical circuit described by a fractional differential equation of the order 0 < α≤ 1. We use the Laplace transform of the fractional derivative in the Caputo sense. In the time domain we emphasize on the delay, rise and settling times, while in the frequency domain the interest is in the cutoff frequency, the bandwidth and the asymptotes in low and high frequencies. All these quantities depend on the order of differential equation.
2
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RLC electrical circuit of non-integer order

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Gómez F., Rosales J., Guía M.
Open Physics
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2013
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vol. 11
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issue 10
1361-1365
EN
In this work a fractional differential equation for the electrical RLC circuit is studied. The order of the derivative being considered is 0 < γ ≤ 1. To keep the dimensionality of the physical quantities R, L and C an auxiliary parameter γ is introduced. This parameter characterizes the existence of fractional components in the system. It is shown that there is a relation between and σ through the physical parameters RLC of the circuit. Due to this relation, the analytical solution is given in terms of the Mittag-Leffler function depending on the order of the fractional differential equation.
3
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Heat conduction in a finite medium using the fractional single-phase-lag model

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Siedlecka U.
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2019
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issue 2
4
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Two dimensional fractional projectile motion in a resisting medium

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Rosales J., Guía M., Gómez F., Aguilar F., Martínez J.
Open Physics
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2014
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vol. 12
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issue 7
517-520
EN
In this paper we propose a fractional differential equation describing the behavior of a two dimensional projectile in a resisting medium. In order to maintain the dimensionality of the physical quantities in the system, an auxiliary parameter k was introduced in the derivative operator. This parameter has a dimension of inverse of seconds (sec)−1 and characterizes the existence of fractional time components in the given system. It will be shown that the trajectories of the projectile at different values of γ and different fixed values of velocity v 0 and angle θ, in the fractional approach, are always less than the classical one, unlike the results obtained in other studies. All the results obtained in the ordinary case may be obtained from the fractional case when γ = 1.
5
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Numerical solution of fractional differential equations by using fractional B-spline

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Jafari H., Khalique C., Ramezani M., Tajadodi H.
Open Physics
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2013
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vol. 11
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issue 10
1372-1376
EN
In this paper, we present fractional B-spline collocation method for the numerical solution of fractional differential equations. We consider this method for solving linear fractional differential equations which involve Caputo-type fractional derivatives. The numerical results demonstrate that the method is efficient and quite accurate and it requires relatively less computational work. For this reason one can conclude that this method has advantage on other methods and hence demonstrates the importance of this work.
6
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An approximation method for fractional integro-differential equations

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Emiroglu I.
Open Physics
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2015
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vol. 13
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issue 1
EN
In this work, an approximation method is proposed for fractional order linear Fredholm type integrodifferential equations with boundary conditions. The Sinc collocation method is applied to the examples and its efficiency and strength is also discussed by some special examples. The results of the proposed method are compared to the available analytic solutions.
7
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Fractional thermal diffusion and the heat equation

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Gómez F., Morales L., González M., Alvarado V., López G.
Open Physics
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2015
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vol. 13
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issue 1
EN
Fractional calculus is the branch of mathematical analysis that deals with operators interpreted as derivatives and integrals of non-integer order. This mathematical representation is used in the description of non-local behaviors and anomalous complex processes. Fourier’s lawfor the conduction of heat exhibit anomalous behaviors when the order of the derivative is considered as 0 < β,ϒ ≤ 1 for the space-time domain respectively. In this paper we proposed an alternative representation of the fractional Fourier’s law equation, three cases are presented; with fractional spatial derivative, fractional temporal derivative and fractional space-time derivative (both derivatives in simultaneous form). In this analysis we introduce fractional dimensional parameters σx and σt with dimensions of meters and seconds respectively. The fractional derivative of Caputo type is considered and the analytical solutions are given in terms of the Mittag-Leffler function. The generalization of the equations in spacetime exhibit different cases of anomalous behavior and Non-Fourier heat conduction processes. An illustrative example is presented.
8
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Numerical approach to the Caputo derivative of the unknown function

100%
Zeng F., Li C.
Open Physics
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2013
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vol. 11
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issue 10
1433-1439
EN
If a function can be explicitly expressed, then one can easily compute its Caputo derivative by the known methods. If a function cannot be explicitly expressed but it satisfies a differential equation, how to seek Caputo derivative of such a function has not yet been investigated. In this paper, we propose a numerical algorithm for computing the Caputo derivative of a function defined by a classical (integer-order) differential equation. By the properties of Caputo derivative derived in this paper, we can change the original typical differential system into an equivalent Caputo-type differential system. Numerical examples are given to support the derived numerical method.
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