Construction of fractal calculus
Weiyi Su · Scientia Sinica Mathematica · 2015
A fractal function does not have the derivatives in Newton sense, however, it still represents some kind of motion and then certainly it has velocity (rate of change). How to construct "fractal calculus" in order to describe the velocity of a fractal function is a challenging and important problem. In this paper, we suggest a principle for establishing new calculus, and according to this principle, as well as by the research results of harmonic analysis and fractal analysis over local elds, we construct "fractal calculus on local elds". Finally, some applications of the fractal calculus are shown.