Application of fractional differentiation to the modeling of hodograph linearities

Abstract

A model for the turbulent boundary layer cross flow velocity component is presented. The model requires the concept of fractional differentiation for a complete description of the conditions imposed on it and also provides an interesting physical picture of the effect of fractional derivatives. The definition of fractional differentiation used here is

$$_o D_x^{m + v} \phi (x) = \frac{{d^{m + 1} }}{{dx^{m + 1} }}\int_o^x {\tfrac{{(x - s)^{ - v} }}{{\Gamma (1 - v)}}\phi (s)ds} $$

where m is a non-negative integer and 0 ≤ v < 1.