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Fractional Pais–Uhlenbeck Oscillator

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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.

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Acknowledgements

The authors would like to that to the referee for his (her) very useful comments and remarks.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey

    Dumitru Baleanu

  2. Institute of Space Sciences, P.O. Box, MG-23, 76900, Magurele-Bucharest, Romania

    Dumitru Baleanu

  3. BERG Faculty, Technical University of Kosice, B. Nemcovej 3, 04200, Kosice, Slovakia

    Ivo Petras

  4. Department of Physics, Tabuk University, P.O. Box 741, Tabuk, 71491, Saudi Arabia

    Jihad H. Asad

  5. Departamento de Matematica Aplicada, Facultad de Matematicas, Universidad Complutense de Madrid, Madrid, 28040, Spain

    Maria Pilar Velasco

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  1. Dumitru Baleanu
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  2. Ivo Petras
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  3. Jihad H. Asad
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  4. Maria Pilar Velasco
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Correspondence to Dumitru Baleanu.

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Baleanu, D., Petras, I., Asad, J.H. et al. Fractional Pais–Uhlenbeck Oscillator. Int J Theor Phys 51, 1253–1258 (2012). https://doi.org/10.1007/s10773-011-1000-y

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  • DOI: https://doi.org/10.1007/s10773-011-1000-y

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