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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
|
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

100%
Gómez F., Rosales J., Guía M.
Open Physics
|
2013
|
vol. 11
|
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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Two dimensional fractional projectile motion in a resisting medium

88%
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.
4
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Fractional thermal diffusion and the heat equation

88%
Gómez F., Morales L., González M., Alvarado V., López G.
Open Physics
|
2015
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vol. 13
|
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.
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