Few-Body Systems

, 58:153 | Cite as

Comparative Study for N D-Dimensional Quantum Oscillators with Respect Fractional Derivative Senses

  • Randa Bekhouche
  • Mohammed Tayeb Meftah
  • Zineb Korichi


In this paper, we focus our study on some systems in statistical mechanics based on the fractional quantum mechanics. At first, we present the partition function of a system composed of N independent fractional quantum oscillators in D-dimensional space. Secondly, based on the three fractional derivatives senses (Liouville, Reimann–Liouville, and Caputo), we calculate the partition function for each sense and we apply the result to 3-dimensional quantum oscillator. By this application, we have shown that the derivative senses, generally, lead to different partition functions.


Fractional derivative Liouville Riemann–Liouville Caputo D-dimensional Quantum oscillator Partition function 


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Copyright information

© Springer-Verlag GmbH Austria 2017

Authors and Affiliations

  • Randa Bekhouche
    • 1
  • Mohammed Tayeb Meftah
    • 1
  • Zineb Korichi
    • 1
  1. 1.LRPPS Laboratory, Faculty of Mathematics and Matter SciencesUniversity of Kasdi MerbahOuarglaAlgeria

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