Abstract :
By considering a coarse-grained space as a space in which the point is not infinitely thin,
but rather has a thickness, one can arrive at an equivalence, on the modeling standpoint,
between coarse-grained space and fractal space. Then, using fractional analysis (slightly
different from the standard formal fractional calculus), one obtains a velocity conversion
formula which converts problems in fractal space to problems in fractal time, therefore
one can apply the corresponding fractional Lagrangian theory (previously proposed by
the author). The corresponding fractal Schrödinger’s equation then appears as a direct consequence
of the usual correspondence rules. In this framework, the fractal generalization of
the Minkowskian pseudo-geodesic is straightforward.
