Analytical study of a pair of coupled mechanical systems without damping by Caputo Fabrizio derivative and the Cuckoo Search optimization algorithm

Autor: Leonardo Martínez Jiménez
Coautor(es): Jorge Mario Cruz-Duarte, Jesús Enrique Escalante-Martínez, J. Juan Rosales-García
Derivatives of non-integer order, also called fractional derivatives, have their origins slightly after the traditional calculus conception about 1695. However, the former had a late development due to its abstraction level and numerical requirements. In recent decades, these two issues have been fulfilled, particularly researchers still pursuing to answer the L'Höpital's question to Leibniz: What does it mean if n = 1/2? "; since n is the order in the Leibniz's derivative notation. Nowadays, it is common to refer as fractional calculus to the branch of mathematical analysis for studying properties and applications of the differential and integral operators of arbitrary order. In this work, we propose a methodology for analyzing mechanical systems, incorporating a model based on fractional differential equations under the Caputo-Fabrizio definition. Moreover, a metaheuristic algorithm is implemented for fitting the model to the experimental data. This technique is Cuckoo Search, which has proven to effective in multiple complex and practical problems. We validate the proposed methodology using an experimental mechanical system and compare its time response against the traditional model and a computational simulation via. Simulink. Results show its feasibility for the accurate description of real systems sans implementing over-complex models.