학술논문
Fractional Pais-Uhlenbeck Oscillator.
Document Type
Article
Author
Source
Subject
*HARMONIC oscillators
*QUANTUM theory
*LAGRANGE equations
*FRACTIONAL calculus
*NUMERICAL analysis
*FUNCTIONAL analysis
*MATHEMATICAL physics
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Language
ISSN
0020-7748
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. [ABSTRACT FROM AUTHOR]