Fractional — Order electrical components, networks and systems

The contemporary curricula of university mathematics contain differential equations of first, second and higher orders. During the last decades however many (mostly non-electrical) disciplines arouse necessitating considerably finer insight into the reality and this fact turned the attention to the (for centuries already known) fractional differential equations with non-integer orders of derivatives like 2/3 or 1.75. Since reliable numerical solution methods like Runge-Kutta or predictor-corrector algorithms do not exist yet, analog electrical networks described by fractional equations can help. The crucial building block of the equation system is then called Constant Phase Element. The paper is devoted to its properties, possible design process, practical realization and some application examples.