Numerical method for determining the order of smallness of the infinitesimal

We investigate infinitesimal quantities (ISQ). ISQ is the main instrument of mathematical analysis and optimization theory. The main characteristic of a ISQ is an order of smallness. The order of smallness is usually rounded to integer, as it is closely associated with derivative functions. The numerical algorithm for finding the fractional order of smallness is proposed. This allows us to find the fractional multiplicity of function roots, fractional derivatives and generalize the criteria for extremes without constraints.