Browsing by Author "Francisco Gomez-Aguilar, Jose"

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Citation Count: Gomez-Aguilar, J.F...et al. (2016). Analytical solutions of the electrical rlc circuit via liouville-caputo operators with local and non-local kernels. Entropy, 18(8). http://dx.doi.org/10.3390/e18080402
Analytical solutions of the electrical rlc circuit via liouville-caputo operators with local and non-local kernels
(MDPI AG, 2016) Francisco Gomez-Aguilar, Jose; Fabian Morales-Delgado, Victor; Antonio Taneco-Hernandez, Marco; Baleanu, Dumitru; Fabricio Escobar-Jimenez, Ricardo; Mohamed Al Qurashi, Maysaa
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 Count: Coronel-Escamilla, Antonio...et al. (2017). Bateman-Feshbach Tikochinsky and Caldirola-Kanai Oscillators with New Fractional Differentiation, Entropy, 19(2).
Bateman-Feshbach Tikochinsky and Caldirola-Kanai Oscillators with New Fractional Differentiation
(MDPI, 2017) Coronel-Escamilla, Antonio; Francisco Gomez-Aguilar, Jose; Baleanu, Dumitru; Cordova Fraga, Teodoro; Fabricio Escobar-Jimenez, Ricardo; Olivares-Peregrino, Victor H.; Al Qurashi, Maysaa Mohamed; 56389
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 Count: Francisco Gomez-Aguilar, Jose...et al. (2017). Chaos in a Cancer Model via Fractional Derivatives with Exponential Decay and Mittag-Leffler Law, ENTROPY, 19(12).
Chaos in a Cancer Model via Fractional Derivatives with Exponential Decay and Mittag-Leffler Law
(MDPI, 2017) Francisco Gomez-Aguilar, Jose; Guadalupe Lopez-Lopez, Maria; Manuel Alvarado-Martinez, Victor; Baleanu, Dumitru; Khan, Hasib; 56389
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 Count: Solis Perez, Jesus Emmanuel...et al. (2018). Chaotic Attractors with Fractional Conformable Derivatives in the Liouville-Caputo Sense and Its Dynamical Behaviors, Entropy, 20(5).
Chaotic Attractors with Fractional Conformable Derivatives in the Liouville-Caputo Sense and Its Dynamical Behaviors
(MDPI, 2018) Solis Perez, Jesus Emmanuel; Francisco Gomez-Aguilar, Jose; Baleanu, Dumitru; Tchier, Fairouz; 56389
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.