To the question of fractional differentiation. Part II

In the paper the investigation continues with the help of definition Fourier fractional differentiation setting in the previous paper “To the question of fractional differentiation”. There were given explicit expressions of a fairly wide class of periodic functions and for functions represented in the form of wavelet decompositions. It was shown that for the class of exponential functions all derivatives with non-integer exponent are equal to zero. The found derivatives have a direct relationship to practical problems and let them use to solve a large class of problems associated with the study of phenomena such as thermal conduction, transmissions, electrical and magnetic susceptibility for a wide range of materials with fractal dimensions.