Browsing by Author "Francisco Gomez-Aguilar, Jose"

Now showing 1 - 7 of 7

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: 12
Citation - Scopus: 12
Anti-Synchronization of Chaotic Systems Using a Fractional Conformable Derivative With Power Law
(Wiley, 2021) Francisco Gomez-Aguilar, Jose; Baleanu, Dumitru; Tchier, Fairouz; Ragoub, Lakhdar; Emmanuel Solis-Perez, Jesus; Solís-Pérez, Jesús Emmanuel; Gómez-Aguilar, José Francisco
In this paper, we propose a new numerical method based on two-step Lagrange polynomial interpolation to get numerical simulations and adaptive anti-synchronization schemes for two fractional conformable attractors of variable order. It was considered the fractional conformable derivative in Liouville-Caputo sense. The novel numerical method was applied to derive new results from the anti-synchronization of the identical uncertain Wang-Sun attractors and three-dimensional chaotic system using fractional conformable sliding mode control. Numerical examples show the effectiveness of the adaptive fractional conformable anti-synchronization schemes for the uncertain chaotic systems considered in this paper.
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: 51
Citation - Scopus: 88
Chaos in a Cancer Model Via Fractional Derivatives With Exponential Decay and Mittag-Leffler Law
(Mdpi, 2017) Guadalupe Lopez-Lopez, Maria; Manuel Alvarado-Martinez, Victor; Baleanu, Dumitru; Khan, Hasib; Francisco Gomez-Aguilar, Jose; Alvarado-Martínez, Victor Manuel; Gómez-Aguilar, José Francisco; López-López, María Guadalupe
In this paper, a three-dimensional cancer model was considered using the Caputo-Fabrizio-Caputo and the new fractional derivative with Mittag-Leffler kernel in Liouville-Caputo sense. Special solutions using an iterative scheme via Laplace transform, Sumudu-Picard integration method and Adams-Moulton rule were obtained. We studied the uniqueness and existence of the solutions. Novel chaotic attractors with total order less than three are obtained.
Citation - WoS: 39
Citation - Scopus: 48
Chaotic Attractors With Fractional Conformable Derivatives in the Liouville-Caputo Sense and Its Dynamical Behaviors
(Mdpi, 2018) Baleanu, Dumitru; Tchier, Fairouz; Solis Perez, Jesus Emmanuel; Francisco Gomez-Aguilar, Jose; Gómez-Aguilar, José Francisco; Pérez, Jesús Emmanuel Solís
This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and beta-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and beta-conformable attractors are provided to illustrate the effectiveness of the proposed method.
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.