Having an approximate realization of the fractance device is an essential part of fractional-order filter design and implementation. This encouraged researchers to introduce many approximation techniques of fractional-order elements. In this paper, the fractional-order KHN low-pass and high-pass filters are investigated based on four different approximation techniques: Continued Fraction Expansion

This paper introduces the concept of fractional-order complex Chebyshev filter. A fractional variation of Chebyshev differential equations is introduced based on Caputo fractional operator. The proposed equation is solved using fractional Taylor power series method. The condition for fractional polynomial solutions is obtained and the first four polynomials scaled using an appropriate scaling

The approximations of fractional-order differentiator/integrator transfer functions are currently performed using integer-order rational functions, which are in general implemented through appropriate multi-feedback topologies. The spreading in the values of time-constants and scaling factors, needed to implement these topologies, increases as the order of the differentiator/integrator and/or the

Multilevel electronic systems offer the reduction of implementation’ complexity, power consumption, and area. Ternary system is a very promising system where more information is represented in the same number of digits compared to the binary systems. In this paper, ternary logic gates and some of their ternary circuit applications are presented using memristors and CNTFET inverter. This

This paper introduces two methods for the numerical solution of distributed order linear fractional differential equations. The first method focuses on initial value problems (IVPs) and based on the αth Caputo fractional definition with the shifted Chebyshev operational matrix of fractional integration. By applying this method, the IVPs are converted into simple linear differential equations which

This paper presents a speech encryption application, which utilizes several proposed generalized modified discrete chaotic maps based on the logistic and tent maps for pseudo-random number generation. The generalization scales the output range and the key space. The modification controls the bounds on the output range through a parameter such that chaotic output exists for almost all values of the

Shared by various physical, chemical, and biological systems, fractional-order dynamics assert that the present state of a system is the result of not only the applied stimulus but also its past history. Consequently, in fractional-order systems, there exists a system-specific, input-dependent memory kernel. In this study, we demonstrate experimentally the existence of a memory effect in electric

Random bit generators (RBGs) in today's digital information and communication systems employ a high rate physical entropy sources such as electronic, photonic, or thermal time series signals. However, the proper functioning of such physical systems is bound by specific constrains that make them in some cases weak and susceptible to external attacks. In this study, we show that the electrical

Recently, double pinch-off points have been discovered in some memristive devices where the I-V hysteresis curve intersects in two points generating triple lobes. This paper investigates a fractional-order flux-controlled mathematical model which is able to develop the multiple pinch-off points or multiple lobes. The conditions for observing double pinch-off points (triple lobes) are derived in

Mathematical Techniques of Fractional Order Systems illustrates advances in linear and nonlinear fractional-order systems relating to many interdisciplinary applications, including biomedical, control, circuits, electromagnetics and security. The book covers the mathematical background and literature survey of fractional-order calculus and generalized fractional-order circuit theorems from