Triple pendulum model involving fractional derivatives with different kernels. (October 2016) - Coronel-Escamilla, A.; Gómez-Aguilar, J.F.; López-López, M.G.; Alvarado-Martínez, V.M.; Guerrero-Ramírez, G.V.
Abstract: The aim of this work is to study the non-local dynamic behavior of triple pendulum-type systems. We use the Euler-Lagrange and the Hamiltonian formalisms to obtain the dynamic models, based on the Riemann-Liouville, Liouville-Caputo, Caputo-Fabrizio and Atangana-Baleanu-Caputo fractional derivative definitions. In these representations, an auxiliary parameter σ is introduced, to define the equations in a fractal temporal geometry, which provides an entire new family of solutions for the dynamic behavior of the pendulum-type systems. The phase diagrams allow to visualize the effect of considering the fractional order approach, the classical behavior is recovered when the order of the fractional derivative is 1.