  Within the framework of fractional calculus with variable order the evolution
of space in the adiabatic limit is investigated. Based on the Caputo definition
of a fractional derivative using the fractional quantum harmonic oscillator a
model is presented, which describes space generation as a dynamic process,
where the dimension $d$ of space evolves smoothly with time in the range 0 <=
d(t) <=3, where the lower and upper boundaries of dimension are derived from
first principles. It is demonstrated, that a minimum threshold for the space
dimension is necessary to establish an interaction with external probe
particles. A possible application in cosmology is suggested.
