Abstract
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.
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