Abstract
This paper presents two evolutionary schemes and a swarm intelligence algorithm for the design of combinational logic circuits. A Genetic and a Memetic schemes as the evolutionary algorithms. The Particle Swarm Optimization as the swarm algorithm. The fitness function used in these three algorithms is sequential, that is, divided in two parts. The first part of the fitness function f(1) evaluates the circuit functionality, while the second part f(2) deals with the circuit complexity. The experiments consist in applying the algorithms in the design of two arithmetic circuits: the one-bit full adder and the one-bit full subtractor. We also present a scalability analysis using the parity checker family of circuits.

Abstract
The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates the higher frequency components of a signal. The SE was first verified by Kelvin in 1887. Since then many researchers developed work on the subject and presently a comprehensive physical model, based on the Maxwell equations, is well established. The Maxwell formalism plays a fundamental role in the electromagnetic theory. These equations lead to the derivation of mathematical descriptions useful in many applications in physics and engineering. Maxwell is generally regarded as the 19th century scientist who had the greatest influence on 20th century physics, making contributions to the fundamental models of nature. The Maxwell equations involve only the integer-order calculus and, therefore, it is natural that the resulting classical models adopted in electrical engineering reflect this perspective. Recently, a closer look of some phenomenas present in electrical systems and the motivation towards the development of precise models, seem to point out the requirement for a fractional calculus approach. Bearing these ideas in mind, in this study we address the SE and we re-evaluate the results demonstrating its fractional-order nature.

Abstract
This paper analyses the performance of a genetic algorithm (GA) in the synthesis of digital circuits using two novel approaches. The first concept consists in improving the static fitness function by including a discontinuity Evaluation. The measure of variability in the error of the Boolean table has similarities with the function continuity issue in classical calculus. The second concept extends the static fitness by introducing a fractional-order dynamical. evaluation. The dynamic-fitness function results from an analogy with control systems where it is possible to benefit the proportional algorithm by including a differential scheme. It is investigated the CA performance when adopting each concept separately. The experiments reveal superior results, in terms of speed and convergence of the number of iterations required to achieve a, solution. In a final phase the two concepts are integrated in the GA fitness function leading to the best performance.

Abstract
This paper analyses the performance of a genetic algorithm using a new concept, namely a fractional-order dynamic fitness function, for the synthesis of combinational logic circuits. The experiments reveal superior results in terms of speed and convergence to achieve a solution.

Abstract
In this work we study a heat diffusion system on a fractional calculus perspective. Several fractional PID tuning methodologies are investigated and compared. The simulations demonstrate the good performance of the proposed fractional algorithm.

Abstract
This paper presents an automated synthesis procedure to design radio-frequency and microwave binary-weighted single-ended switched capacitor arrays (RFSSCAs) from user top-level specifications to components sizes. The method relies on closed-form symbolic mathematical expressions of the input impedance and quality factor of the RFSSCA. The genetic synthesis tool optimizes a fitness function based on user-specified performance constraints. The method determines several optimal solutions, which are completely independent of the starting point. Moreover, infeasible specifications are unambiguously detected. To validate the proposed design algorithm, two RFSSCAs are synthesized in a 0.35 mu m CMOS technology and verified by the SpectreRF simulator of the Cadence design environment. The results show that the synthesis and simulation outcomes are in very good agreement.