Browsing by Author "Escobar-Jiménez, Ricardo Fabricio"

Now showing 1 - 3 of 3

Citation - WoS: 75
Citation - Scopus: 110
Analytical Solutions of the Electrical Rlc Circuit Via Liouville-Caputo Operators With Local and Non-Local Kernels
(Mdpi, 2016) Fabian Morales-Delgado, Victor; Antonio Taneco-Hernandez, Marco; Baleanu, Dumitru; Fabricio Escobar-Jimenez, Ricardo; Mohamed Al Qurashi, Maysaa; Francisco Gomez-Aguilar, Jose; Taneco-Hernández, Marco Antonio; Al Qurashi, Maysaa Mohamed; Morales-Delgado, Victor Fabian; Gómez-Aguilar, José Francisco; Escobar-Jiménez, Ricardo Fabricio
In this work we obtain analytical solutions for the electrical RLC circuit model defined with Liouville-Caputo, Caputo-Fabrizio and the new fractional derivative based in the Mittag-Leffler function. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. Different source terms are considered in the fractional differential equations. The classical behaviors are recovered when the fractional order a is equal to 1.
Citation - WoS: 45
Citation - Scopus: 60
Bateman-Feshbach Tikochinsky and Caldirola-Kanai Oscillators With New Fractional Differentiation
(Mdpi, 2017) Francisco Gomez-Aguilar, Jose; Baleanu, Dumitru; Cordova-Fraga, Teodoro; Fabricio Escobar-Jimenez, Ricardo; Olivares-Peregrino, Victor H.; Al Qurashi, Maysaa Mohamed; Coronel-Escamilla, Antonio; Gómez-Aguilar, José Francisco; Escobar-Jiménez, Ricardo Fabricio
In this work, the study of the fractional behavior of the Bateman-Feshbach-Tikochinsky and Caldirola-Kanai oscillators by using different fractional derivatives is presented. We obtained the Euler-Lagrange and the Hamiltonian formalisms in order to represent the dynamic models based on the Liouville-Caputo, Caputo-Fabrizio-Caputo and the new fractional derivative based on the Mittag-Leffler kernel with arbitrary order . Simulation results are presented in order to show the fractional behavior of the oscillators, and the classical behavior is recovered when is equal to 1.
Citation - WoS: 23
Citation - Scopus: 26
Formulation of Euler-Lagrange and Hamilton Equations Involving Fractional Operators With Regular Kernel
(Springeropen, 2016) Francisco Gomez-Aguilar, Jose; Baleanu, Dumitru; Fabricio Escobar-Jimenez, Ricardo; Hugo Olivares-Peregrino, Victor; Abundez-Pliego, Arturo; Coronel-Escamilla, Antonio; Olivares-Peregrino, Victor Hugo; Gómez-Aguilar, José Francisco; Escobar-Jiménez, Ricardo Fabricio
This paper presents alternative representations to traditional calculus of the Euler-Lagrangian equations, in the alternative representations these equations contain fractional operators. In this work, we consider two problems, the Lagrangian of a Pais-Uhlenbeck oscillator and the Hamiltonian of a two-electric pendulum model where the fractional operators have a regular kernel. The Euler-Lagrange formalism was used to obtain the dynamic model based on the Caputo-Fabrizio operator and the new fractional operator based on the Mittag-Leffler function. The simulations showed the effectiveness of these two representations for different values of gamma.