The author introduces functions
are Airy functions of the first and second kind, respectively. He proves that half integral of the Airy functions
is the Scorer function) can be expressed in the terms of
Based on that the author establishes general formulas for computing semi-integral derivatives of
. Here the functional derivatives of order
of the function
is the Fourier transform of the function
. Some applications to Korteweg-de Vries type equations and for the Ostrovsky equation are given.