This article analyzes parallel resonant circuit containing fractional capacitor and inductor. Relations for complex impedance, resonant frequency, and resistance at this frequency are derived. These formulas are then expressed graphically. The influence of the exponents of frequency dependence of impedance α and β is especially emphasized which is not present when classical elements are used. The possibilities of practical implementation of fractional elements are introduced whereas RC elements with distributed parameters are preferred. An example of fractional capacitor made by thick-film technology is shown and rules for finding its parameters are stated.