Fractional Order Circuits and Systems


Ahmed Madian

Faculty of Engineering and Applied Science, NILE University, Giza, Egypt

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Fractional calculus, as generalization of integer-order calculus to its fractional-order, has demonstrated to be a valuable tool in the modeling of many applications in physics, electronic circuits, biomaterials, and electrochemistry. Recently, there has been an increasing need to merge the fundamentals of fractional calculus into many engineering applications in an interdisciplinary way showing the advantages of fractional-order relative to conventional integer-order systems. 

For example, the capability of step less control of the slope of frequency characteristics in fractional-order filters in comparison with the corresponding integer-order filters is an attractive feature. Fractional-order impedance circuits are also very promising in modeling electrical properties of biological materials, tissues or cells. Oscillators of fractional-order provide possibility of obtaining higher oscillation frequencies compared to the integer-order counterparts with the same values of passive element parameters offering arbitrary phase shift between output signals. 

This talk deals with the design and realization of analog and digital integrated fractional-order circuits, which offer the benefits: (i) capability of on-chip implementation, (ii) capability of low-voltage operation, and (iii) electronic adjustment of their characteristics. 

The demonstrated applications include fractional-order systems suitable for biomedical signal processing, for neuromorphic applications, for modeling biological tissues, for realizing fractional-order PID controllers etc.