Fractional calculus has been proved through numerous research examples to be a superior tool for system description than the narrow integer order domain. This is achieved through the extra parameters introduced via allowing the differential or integral orders to take non-integer values. The promising capabilities of fractional-order devices challenge the research to find a way to simulate its behavior until its off-shelf appearance. Different integer order approximation techniques to the fractional-order transfer functions are investigated in the literature. The main idea behind approximating the fractance device is to achieve a nearly constant phase response of the impedance. There are many categories of fractional order system approximations in analog and digital domains.

Research in circuits and systems using fractional-order elements is considered as an interdisciplinary topic. It serves many areas of applications such as electrical engineering, medicine, physics, control system, chaos theory signal processing, and bio-impedance.

In bioengineering, conventional lumped element circuit models of tissue were extended as fractional-order generalization through modification of the defining current-voltage relationships. Such fractional-order models provide an improved description of observed bio-impedance behavior. Electrical impedance measurements have been widely used to estimate plant health, maturity of fruits, fruit damages, and structural cellular variation during fruit ripening, freeze or chill damages, and measurement of tree root growth. These analyses may be used in the field of importing and exporting fruits and vegetables.

Generalizing the chaotic system to the fractional-order domain increases the rate of complexity level and provides more degrees of freedom in both the time and the frequency domain. In order to get higher performance, fractional-order has emerged in different chaotic systems. The fractional-order chaotic systems increase the chaotic behavior in new dimensions and add extra degrees of freedom, which increases system controllability. Fractional-order chaotic systems parameter identification is an essential issue in chaos control and synchronization process.

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