D-Dimensional Statistical Mechanics in Fractional Classical and Quantum Mechanics

Résumé

In this work, we focus our study on some systems in statistical mechanics based on the fractional classical and quantum mechanics in any positive spatial dimension D. At the first stage we present the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In each case, the Hamiltonian exhibits fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac.