INTRODUCTION TO WAVE PHENOMENA AND UNCERTAINTY IN A FRACTAL SPACE .1.

The purpose of this note is to introduce the principle of dynamics in a fractal space. Although a lot of work has been devoted to fractal geometry, the introduction of time with regard to a fractal space must not be undertaken without some restrictions. In a first step, our analysis restricts itself to the case of electromagnetic theory which will be described in terms of differential geometry and homologic algebra. By an appropriate extension, some efficient mathematical tools, like the fractional derivative operator, will be introduced to enlarge dynamics to 'fractal dynamics' or, more generally speaking, to 'scale dynamics'. This analysis enlightens the opportunities opened by the fractional derivative in quantum mechanics and, at the same time, restrains the generalisation. It is shown that one of the authorised generalisations is related to the 'uncertainty principle' which can be considered as a 'universal principle' concerning the defect of accuracy of the analysis with respect to a physical phenomenon. In the frame of quantum mechanics, the approach puts the emphasis on some conclusions that deal with the use of such operators and some adequate extension.