Abstract
A study of the fractional Lagrangian of the so-called Caldirola-Kanai oscillator is presented. The fractional Euler-Lagrangian equations of the system have been obtained, and the obtained Euler-Lagrangian equations have been studied numerically. The numerical study is based on the so-called Grunwald-Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grunwald-Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman-Liouville fractional derivative is equivalent to the Grunwald-Letnikov derivative for a wide class of the functions.