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In this paper, we analyse the robustness of the fractional wave equation with a fractional-order boundary controller subject to delayed boundary measurement. [ABSTRACT FROM AUTHOR]

Based on a electromechanical system to be digitally controlled, this paper shows how to add an anti-windup feature to a third-generation CRONE controller. [ABSTRACT FROM AUTHOR]

Many modifications have been proposed to improve the Smith predictor structure used to control plant with time-delay. [ABSTRACT FROM AUTHOR]

This paper concerns the application of flatness principle to fractional systems. In path planning, the flatness concept is used when the trajectory is fixed (in space and in time), to determine the controls inputs to apply without having to integrate any differential equations. [ABSTRACT FROM AUTHOR]

A new method to control single-link lightweight flexible manipulators in the presence of changes in the load is proposed in this paper. The overall control scheme consists of three nested control loops. Once the friction and other nonlinear effects have been compensated, the inner loop is designed to give a fast motor response. The middle loop decouples the dynamics of the system, and reduces its transfer function to a double integrator. [ABSTRACT FROM AUTHOR]

A new approach to path tracking using a fractional differentiation prefilter applied to nonvarying plants is proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper tuning rules for fractional proportional-integral-derivative (PID) controllers similar to (though more complex than) those proposed by Ziegler and Nichols (for integer PID controllers) are presented. [ABSTRACT FROM AUTHOR]

Recently, active wave control theory has attracted great interest as a novel method for vibration control of large space structure (LSS). [ABSTRACT FROM AUTHOR]

In the present study non-integer order or fractional derivative rheological models are applied to the dynamical analysis of mechanical systems. [ABSTRACT FROM AUTHOR]

The notions of linear matrix inequalities (LMI) and convexity are strongly related. [ABSTRACT FROM AUTHOR]

Fractional-order derivatives appear in various engineering applications including models for viscoelastic damping. Damping behavior of materials, if modeled using linear, constant coefficient differential equations, cannot include the long memory that fractional-order deriative require. [ABSTRACT FROM AUTHOR]

New generalization of fractals named as quasi-fractals (QF) is introduced for description of wide class of disordered media. [ABSTRACT FROM AUTHOR]

The nonlinear force-displacement relations of a viscoelastic cylindrical column under uniaxial monotonic slow compressive displacement with a constant speed, and under uniaxial rapid sinusoidal displacement with a constant compressive predisplacement were experimentally and theoretically investigated to describe fractional derivative models for these relations. They were separately extracted from the slow compressive and the rapid sinusoidal experiments. These fractional derivative models were combined to construct a unified nonlinear viscoelastic model to cover from slow to rapid phenomenon appeared in the test specimen. This model successfully reproduced the slow and the rapid phenomena in the experiment. [ABSTRACT FROM AUTHOR]

This paper develops the concept of the complex order-distribution. This is a continuum of fractional differintegrals of complex order. Two types of complex order-distributions are considered, uniformly distributed and Gaussian distributed. It is shown that these basis distributions can be summed to approximate other complex order-distributions. [ABSTRACT FROM AUTHOR]

Hardware implementation of fractional-order differentiators and integrators requires careful consideration of issues of system quality, hardware cost, and speed. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The use of fractional differentiation in vehicle suspension design has many interests. This paper presents a hydropneumatic suspensions design method based on fractional differentiation. Once a hydraulic structure has been chosen for the suspension, it is possible to calculate the values of all technological parameters, so that the suspension force - deflection transfer function is a band-limited fractional differentiator. The combination of the CRONE control methodology and hydropneumatic technology leads to remarkable performances of robustness. Keywords Fractional differentiation, hydropneumatic technology, CRONE control, hydropneumatic test bench. [ABSTRACT FROM AUTHOR]

This study talks about gastrocnemius muscle identification. During biological activation, every contractile structure is unsynchronized. Likewise, contraction and relaxation phases depend on all contractile elements, the activation type and the state of health. Moreover, gastrocnemius muscle is composed of three fibre types: fast (IIB), resistant (IIA), and slow (I) fibres. [ABSTRACT FROM AUTHOR]

The so-called fractional relaxor-oscillator, whose time evolution is characterized by an index of fractional order,α, exhibits interesting relaxationoscillation characteristics. [ABSTRACT FROM AUTHOR]

Cole-Cole systems are widely used in electrochemistry to represent impedances of galvanic elements like fuel cells. [ABSTRACT FROM AUTHOR]

Some existing methods for identifying models from frequency data (Levy's method without and with weights, and its improvements by Sanathanan and Koerner and by Lawrence and Rogers) are extended to deal with fractional models. Keywords Identification, fractional-order systems, Levy's method. [ABSTRACT FROM AUTHOR]

Understanding and modeling transport of solutes in porous media is a critical issue in the environmental protection. The common model is the advective-dispersive equation (ADE) describing the superposition of the advective transport and the Brownian motion in water-filled pore space. [ABSTRACT FROM AUTHOR]

Heat transfer problems obey to diffusion phenomenon. They can be modelled with the help of fractional systems. [ABSTRACT FROM AUTHOR]

Solute spreading is studied, in saturated but heterogeneous porous media. The solid matrix is assumed to be composed of bounded obstacles, and the logarithm of the porosity is supposed to be represented by a three-dimensional random process. The latter appears as a parameter in the equation, ruling solute spreading, on the small scale. The concentration of solute, averaged with respect to the process, satisfies an equation which resembles Fourier's law, except that it involves a term, non-local with respect to time. [ABSTRACT FROM AUTHOR]

We show that the space-fractional advection-diffusion equation arising from the large-scale dynamics of Lévy walks has to be modified when a boundary condition is imposed. In particular, we study the case of a reflective barrier constraining the diffusing particles to a semi-infinite domain. [ABSTRACT FROM AUTHOR]

It is proved that kinetic equations containing noninteger integrals and derivatives are appeared in the result of reduction of a set of micromotions to some averaged collective motion in the mesoscale region. Key words Generalized Riemann-Liouville fractional integral, universal decoupling procedure. [ABSTRACT FROM AUTHOR]

This paper gives a short review about the application of semi-integrals to the Abel-type integral transform with the kernel (t2 - x2)-1/2 Keywords Fractional calculus, integral equations, particle accelerators, beam, diagnostics, quantum mechanics, spin. [ABSTRACT FROM AUTHOR]

The paper provides the fractional Lagrangian and Hamiltonian formulations of mechanical and field systems. The fractional treatment of constrained system is investigated together with the fractional path integral analysis. Fractional Schrüdinger and Dirac fields are analyzed in details. Keywords Fractional calculus, fractional variational principles, fractional Lagrangian and Hamiltonian, fractional Schrödinger field, oing fractional Dirac field. [ABSTRACT FROM AUTHOR]

The phenomenon of stickiness of the dynamical trajectories to the domains of periodic orbits (islands), or simply to periodic orbits, can be considered a primary source of the fractional kinetic equation (FKE). An additional condition for the FKE occurrence is a property of the corresponding sticky domains to have space-time invariance under the space-time renormalization transform. The dynamics in some class of polygonal billiards is pseudochaotic (i.e., dynamics is random but the Lyapunov exponent is zero), and the corresponding features of the self-similarity are reflected in the discrete space-time renormalization invariance. We consider an example of such a billiard and its dynamical and kinetic properties that leads to the FKE. Keywords Fractional kinetics, pseudochaos, recurrences, billiards. [ABSTRACT FROM AUTHOR]

Generalised fractional centred differences and derivatives are studied in this chapter. Keywords Fractional centred difference, fractional centred derivative, Grünwald-Letnikov derivative, generalised Cauchy derivative. [ABSTRACT FROM AUTHOR]

Key words Fractional differential equations, Caputo, Riemann-Liouville, linear. [ABSTRACT FROM AUTHOR]

In this paper, we propose a procedure to achieve pseudo-rational approximation to arbitrary fractional-order linear time invariant (FO-LTI ) systems with suboptimum H -norm. [ABSTRACT FROM AUTHOR]

This paper presents a comparative study of the performance of five different numerical schemes for the solution of fractional differential equations. [ABSTRACT FROM AUTHOR]

Recognizing the importance of proper initialization of a system, which is evolving in time according to a differential equation of fractional order, Lorenzo and Hartley developed the method of properly incorporating the effect of the past (history) by means of an initialization function for the Riemann-Liouville and the Grunwald formulations of fractional calculus. The present work addresses this issue for the Caputo fractional derivative and cautions that the commonly held belief that the Caputo formulation of fractional derivatives properly accounts for the initialization effects is not generally true when applied to the solution of fractional differential equations. Key words Caputo fractional derivatives, initialization issues. [ABSTRACT FROM AUTHOR]

The Mittag-Leffler function Eα(z), which is a generalization of the exponential function, arises frequently in the solutions of physical problems described by differential and/or integral equations of fractional order. Consequently, the zeros of Eα (z) and their distribution are of fundamental importance and play a significant role in the dynamic solutions. The Mittag- Leffler function E (z) is known to have a finite number of real zeros in the range 1 < α > 2 which is applicable for many physical problems. What has not been known is the exact number of real zeros of Eα (z) for a given value of α in this range. An iteration formula is derived for calculating the number of real zeros of Eα(z) for any value of α in the range 1 < α > 2 and some specific results are tabulated. Key words Mittag-Leffler functions, zeros, fractional calculus. [ABSTRACT FROM AUTHOR]

We have recently presented elsewhere a Galerkin approximation scheme for fractional order derivatives, and used it to obtain accurate numerical solutions of second-order (mechanical) systems with fractional-order damping terms. Keywords Fractional derivative, Galerkin, finite element, Basset's problem, relaxation, creep. [ABSTRACT FROM AUTHOR]