  In this paper, we study the effect of non-local derivative on Bose-Einstein
condensation. Firstly, we consider the Caputo-Fabrizio derivative of fractional
order \alpha to derive the eigenvalues of non-local Schr\"odinger equation for
a free particle in a 3D box. Afterwards, we consider 3D Bose-Einstein
condensation of an ideal gas with the obtained energy spectrum. Interestingly,
in this approach the critical temperatures Tc of condensation for 1 < \alpha <
2 are greater than the standard one. Furthermore, the condensation in 2D is
shown to be possible. Second and for comparison, we presented, on the basis of
a spectrum established by N. Laskin, the critical transition temperature as a
function of the fractional parameter {\alpha} for a system of free bosons
governed by an Hamiltonian with power law on the moment (H~p\alpha). In this
case, we have demonstrated that the transition temperature is greater than the
standard one. By comparing the two transition temperatures (relative to
Caputo-Fabrizio and to Laskin), we have found for fixed \alpha and the density
\rho that the transition temperature relative to Caputo-fabrizio is greater
than relative to Laskin.
