A TLM Formulation Based on Fractional Derivatives for Dispersive Cole-Cole Media

An auxiliary differential equation (ADE) transmission line method (TLM) is proposed for broadband modeling of electromagnetic (EM) wave propagation in biological tissues with the Cole-Cole dispersion Model. The fractional derivative problem is surmounted by assuming a linear behavior of the polarization current when the time discretization is short enough. The polarization current density is approached using Lagrange extrapolation polynomial and the fractional derivation is obtained according to Riemann definition of a fractional α -order derivative. Reflection coefficients at an air/muscle and air/fat tissues interfaces simulated in a 1-D domain are found to be in good agreement with those obtained from the analytic model over a broad frequency range, demonstrating the validity of the proposed approach.

On an extension of Hadamard fractional derivative

In this paper, we introduce a new approach to the fractional derivation which generalizes the classical Hadamard fractional derivative. We prove some properties of this new approach and also establish some results by addressing some standard functions.

Convolution Algebraic Structures Defined by Hardy-Type Operators

The main aim of this paper is to show that certain Banach spaces, defined via integral kernel operators, are Banach modules (with respect to some known Banach algebras and convolution products onℝ+). To do this, we consider some suitable kernels such that the Hardy-type operator is bounded in weighted Lebesgue spacesLωpℝ+forp≥1. We also show new inequalities in these weighted Lebesgue spaces. These results are applied to several concrete function spaces, for example, weighted Sobolev spaces and fractional Sobolev spaces defined by Weyl fractional derivation.

Path Tracking Design by Fractional Prefilter Extension to Square MIMO Systems

The aim of this paper concerns motion control and robust path tracking. An approach based on fractional prefilter synthesis was already developed. It allows tracking optimization according to the fractional derivation order, the actuators physical constraints and the control loop frequency bandwidth. The purpose of this paper is the extension of this approach to multivariable systems. A non integer prefilter synthesis methodology for square MIMO systems (Multi-Input, Multi-Output) is presented. It is based on the MIMO-QFT robust synthesis methodology, taking into account of the plant uncertainties. MIMO-QFT robust synthesis methodology is based on multiple SISO (MISO systems) synthesis by considering the loop couplings. The SISO-QFT synthesis methodology can be then used for each SISO synthesis. Then the prefilters are synthesized. The prefilter parameter optimization is founded on the prefilter output error integral minimization, taking into account of the actuators physical constraints and the tracking performance specifications. An application example is given.