Comments on ‘‘Modeling fractional stochastic systems as non-random fractional dynamics driven Brownian motions

Applied Mathematical Modelling, Vol.33

Introduction to fractional linear systems. Part 1 : continuous-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Introduction to fractional linear systems. Part 2: discrete-time case

IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1

Numerical prediction of diffusion and electric field-induced iron nanoparticle transport

Zero valent iron nanoparticles (nZVI) are considered very promising for the remediation of contaminated soils and groundwaters. However, an important issue related to their limited mobility remains unsolved. Direct current can be used to enhance the nanoparticles transport, based on the same principles of electrokinetic remediation. In this work, a generalized physicochemical model was developed and solved numerically to describe the nZVI transport through porous media under electric field, and with different electrolytes (with different ionic strengths). The model consists of the Nernst–Planck coupled system of equations, which accounts for the mass balance of ionic species in a fluid medium, when both the diffusion and electromigration of the ions are considered. The diffusion and electrophoretic transport of the negatively charged nZVI particles were also considered in the system. The contribution of electroosmotic flow to the overall mass transport was included in the model for all cases. The nZVI effective mobility values in the porous medium are very low (10−7–10−4 cm2 V−1 s−1), due to the counterbalance between the positive electroosmotic flow and the electrophoretic transport of the negatively charged nanoparticles. The higher the nZVI concentration is in the matrix, the higher the aggregation; therefore, low concentration of nZVI suspensions must be used for successful field application.

An introduction to the fractional continuous-time linear systems

A brief introduction to the fractional continuous-time linear systems is presented. It will be done without needing a deep study of the fractional derivatives. We will show that the computation of the impulse and step responses is very similar to the classic. The main difference lies in the substitution of the exponential by the Mittag-Leffler function. We will present also the main formulae defining the fractional derivatives.

On the fractional central differences and derivatives

Fractional central differences and derivatives are studied in this article. These are generalisations to real orders of the ordinary positive (even and odd) integer order differences and derivatives, and also coincide with the well known Riesz potentials. The coherence of these definitions is studied by applying the definitions to functions with Fourier transformable functions. Some properties of these derivatives are presented and particular cases studied.

An introduction to the fractional continuous- time linear systems: the 21st century systems

IEEE CIRCUITS AND SYSTEMS MAGAZINE, Third Quarter

Fractional central differences and derivatives

Journal of Vibration and Control, Vol. 14, Nº 9-10

On the relation between the fractional Brownian motion and the fractional derivatives

Physics Letters A, vol. 372; Issue 7

A new least-squares approach to differintegration modeling

Signal Processing, Vol. 86, nº 10

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

Pseudo-fractional ARMA modelling using a double Levinson recursion

IET Control Theory & Applications, Vol. 1, Nº 1

A new symmetric fractional B-spline

Signal Processing, Vol. 83, nº 11

On the initial conditions in continuous-time fractional linear systems

Signal Processing, Vol. 83, nº 11

Fractional discrete-time signal processing: scale conversion and linear prediction

Nonlinear Dynamics, Vol. 29