Fractional Pais-Uhlenbeck Oscillator

Abstract

In this paper we study the fractional Lagrangian of Pais–Uhlenbeck oscillator. We obtained the fractional Euler–Lagrangian equation of the system and then we studied the obtained Euler–Lagrangian equation numerically. The numerical study is based on the so-called Grünwald–Letnikov approach, which is power series expansion of the generating function (backward and forward difference) and it can be easy derived from the Grünwald– Letnikov definition of the fractional derivative. This approach is based on the fact, that Riemman–Liouville fractional derivative is equivalent to the Grünwald–Letnikov derivative for a wide class of the functions