251. Fractional Pais–Uhlenbeck Oscillator
- Author
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María Velasco, Jihad H. Asad, Dumitru Baleanu, and Ivo Petras
- Subjects
Power series ,symbols.namesake ,Physics and Astronomy (miscellaneous) ,General Mathematics ,Mathematical analysis ,symbols ,Finite difference ,Generating function ,Derivative ,Lagrangian ,Fractional calculus ,Mathematics - 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 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.
- Published
- 2011
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