Abstract

GOMEZ-AGUILAR, J.F. et al. Fractional mechanical oscillators. Rev. mex. fis. [online]. 2012, vol.58, n.4, pp.348-352. ISSN 0035-001X.

In this contribution we propose a new fractional differential equation to describe the mechanical oscillations of a simple system. In particular, we analyze the systems mass-spring and spring-damper. The order of the derivatives is 0 < γ ≤ 1. In order to be consistent with the physical equation a new parameter σ is introduced. This parameter characterizes the existence of fractional structures in the system. A relation between the fractional order time derivative γ and the new parameter a is found. Due to this relation the solutions of the corresponding fractional differential equations are given in terms of the Mittag-Leffler function depending only on the parameter γ. The classical cases are recovered by taking the limit when γ = 1.

Keywords : Fractional calculus; mechanical oscillators; caputo derivative; fractional structures.