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Browsing by Author "Rosales Garcia, J. Juan"

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    Citation - WoS: 4
    Analysis of Drude Model Using Fractional Derivatives Without Singular Kernels
    (de Gruyter Open Ltd, 2017) Rosales Garcia, J. Juan; Ortega Contreras, Abraham; Baleanu, Dumitru; Martinez Jimenez, Leonardo; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    We report study exploring the fractional Drude model in the time domain, using fractional derivatives without singular kernels, Caputo-Fabrizio (CF), and fractional derivatives with a stretched Mittag-Leffer function. It is shown that the velocity and current density of electrons moving through a metal depend on both the time and the fractional order 0 < gamma <= 1. Due to non-singular fractional kernels, it is possible to consider complete memory effects in the model, which appear neither in the ordinary model, nor in the fractional Drude model with Caputo fractional derivative. A comparison is also made between these two representations of the fractional derivatives, resulting a considered difference when gamma < 0.8.
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    Citation - WoS: 43
    Citation - Scopus: 40
    Motion of a Particle in a Resisting Medium Using Fractional Calculus Approach
    (Editura Acad Romane, 2013) Rosales Garcia, J. Juan; Baleanu, Dumitru; Guia Calderon, M.; Martinez Ortiz, Juan; Baleanu, Dumitru; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
    In this manuscript we propose a fractional differential equation to describe the vertical motion of a body through the air. The order of the derivative was considered to be 0 < gamma <= 1. To keep the dimensionality of the physical parameter in the system, an auxiliary parameter sigma is introduced. This parameter characterizes the existence of fractional components in the given system. We prove that there is a relation between gamma and sigma through the physical parameter of the system and that, due to this relation the analytical solutions are given in terms of the Mittag-Leffler function depending on the order of the fractional differential equation.