Fractal system — A time domain approach

A method to analyze the fractal system in the time domain is presented so that the dynamic behavior of the system can be studied. The fractal system is represented by a set of linear time-varying differential equations whose order depends on the order of the system under non-fractal condition. Four different types of fractal system are considered and their solutions in the time domain are presented. These analyses show that the fractal system is dynamically more stable with smooth changes of magnitude and less oscillatory than the non-fractal system. Examples of the physiological system of the conduction pathways in the heart and also the polarization phenomena of noble metal are presented to illustrate the phonomena.