LAUSR

Abstract In this paper, we investigate the fractional version of the one-dimensional relativistic oscillators. We apply some important definitions and properties of a new kind of fractional formalism on the Dirac oscillator (DO). By using a semiclassical approximation, the energy eigenvalues have been determined for the oscillator. The obtained results show a remarkable influence of the fractional parameter on the energy eigenvalues. By considering a unique energy spectrum, we present a simple numerical computation of the thermal properties of a defined energy spectrum of a system. the Euler–Maclaurin formula has been used to calculate the partition function and therefore the associated thermodynamics quantities. In addition, the eigensolutions of the fractional Dirac oscillator, based on the factorization method, have been determined.