Investigation of classical and fractional Bose-Einstein condensation for harmonic potential

► We investigate Bose-Einstein Condensation for real systems. ► Fractional Gross-Pitaevskii equations were written using the Caputo fractional derivative operator. ► Classical and fractional Gross-Pitaevskii equations were solved with the Homotopy Perturbation Method. ► We consider that fractional Gross-Pitaevskii equations can describe the inhomogeneous, irreversible and non-unitary systems.