Browsing by Author "Hugo Olivares-Peregrino, Victor"

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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.
Citation - WoS: 102
Citation - Scopus: 114
Laplace Homotopy Analysis Method for Solving Linear Partial Differential Equations Using a Fractional Derivative With and Without Kernel Singular
(Springeropen, 2016) Francisco Gomez-Aguilar, Jose; Yepez-Martinez, Huitzilin; Baleanu, Dumitru; Fabricio Escobar-Jimenez, Ricardo; Hugo Olivares-Peregrino, Victor; Fabian Morales-Delgado, Victor; Olivares-Peregrino, Victor Hugo; Morales-Delgado, Victor Fabian; Gómez-Aguilar, José Francisco; Escobar-Jimenez, Ricardo Fabricio
In this work, we present an analysis based on a combination of the Laplace transform and homotopy methods in order to provide a new analytical approximated solutions of the fractional partial differential equations (FPDEs) in the Liouville-Caputo and Caputo-Fabrizio sense. So, a general scheme to find the approximated solutions of the FPDE is formulated. The effectiveness of this method is demonstrated by comparing exact solutions of the fractional equations proposed with the solutions here obtained.