The Minkowski's space–time is consistent with differential geometry of fractional order

The recent discovery of fractional Taylor's series for nondifferentiable functions, f(x+h)=Eα(hαDxα)f(x), where Eα(⋅)Eα(⋅) denotes the Mittag-Leffler function, and Dxα is the so-called modified Riemann–Liouville fractional derivative, opens the possibility of a differential geometry of fractional order. It is shown that the Lorentz pseudo-metric is quite consistent with this fractional geometry, in other words that the fractional velocity of light does not affect the matter. The fractal effect is pictured by change of scale in space and time.