The power-law conductivity sigma proportional to omega(a) (0 < a < 1), seen in various organic thin films, can be utilized as a novel category of circuit elements against the conventional three, i.e. resistors, capacitors and inductors. This novel category, referred to as the "fractal device", acts as a noninteger-rank differential/integral operator with a unique memory effect in the electronic circuits. The present paper reports the fundamentals of the fractal device and the guidelines on hardware realization of it in the form of thin film device based on molecular assemblies.