 Triple pendulum model involving fractional derivatives with different kernelsA. Coronel-Escamilla, J.F. Gómez-Aguilar, M.G. López-López, V.M. Alvarado-Martínez and G.V. Guerrero-Ramírez Chaos, Solitons & Fractals, 2016, vol. 91, issue C, 248-261 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. Keywords: Fractional dynamics; Riemann-Liouville derivative; Liouville-Caputo derivative; Caputo-Fabrizio derivative; Atangana-Baleanu derivative; Adams-Bashforth-Moulton method; Lagrangian dynamics; Hamilton equations (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:91:y:2016:i:c:p:248-261 DOI: 10.1016/j.chaos.2016.06.007 Access Statistics for this article Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros More articles in Chaos, Solitons & Fractals from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.