Triple pendulum model involving fractional derivatives with different kernels

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...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2016-10, Vol.91, p.248-261
Main Authors: Coronel-Escamilla, A., Gómez-Aguilar, J.F., López-López, M.G., Alvarado-Martínez, V.M., Guerrero-Ramírez, G.V.
Format: Article
Language:English
Subjects:
Adams-Bashforth-Moulton method
Atangana-Baleanu derivative
Caputo-Fabrizio derivative
Fractional dynamics
Hamilton equations
Lagrangian dynamics
Liouville-Caputo derivative
Riemann-Liouville derivative
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Summary: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.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2016.06.007