Triple pendulum model involving fractional derivatives with different kernels. (October 2016)

• Record Type: Journal Article
• Authors: Coronel-Escamilla, A.; Gómez-Aguilar, J.F.; López-López, M.G.; Alvarado-Martínez, V.M.; Guerrero-Ramírez, G.V.
• Is Part Of: Chaos, solitons and fractals. Volume 91(2016)
• Page Start: 248
• Page End: 261
• Publication Date: 2016-10
• Subjects: Fractional dynamics -- Riemann-Liouville derivative -- Liouville-Caputo derivative -- Caputo-Fabrizio derivative -- Atangana-Baleanu derivative -- Adams-Bashforth-Moulton method -- Lagrangian dynamics -- Hamilton equations; 26A33 -- 65R10 -- 70Hxx; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2016.06.007
• Languages: English
• ISSNs: 0960-0779

Abstract

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.