Investigation of fractional harmonic oscillator canonical ensemble in the q-deformed super-statistic

Abstract

In this paper, a canonical ensemble of fractional harmonic oscillator has been considered. Then by using the q-deformed formalism of super-statistic, thermodynamical properties of such an ensemble have been evaluated. The important point in this paper is that because of the existence of the fractional parameter, the partition functions, consequently and the other thermodynamical properties, can be analytically derived. Therefore, these quantities have been evaluated numerically. These quantities have been plotted in terms of temperature when the deformation and the fractional parameter vary. Effects of these parameters on the thermodynamical properties of the canonical ensemble have been discussed in detail.