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

Physics Letters A, vol. 372; Issue 7

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

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

A signal processing view of differintegration

Proceedings of the European Control Conference, ECC’01, Porto, Portugal, September 2001

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

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.

Fractional central differences and derivatives

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

A new symmetric fractional B-spline

Signal Processing, Vol. 83, nº 11

Fractional central differences and derivatives

Journal of Vibration and Control, 14(9–10): 1255–1266, 2008

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

Applied Mathematical Modelling, Vol.33

On the initial conditions in continuous-time fractional linear systems

Signal Processing, Vol. 83, nº 11

Synthesis and characterization of C3-symmetric 1,3,5 - Benzenetricarboxamide derived supramolecular systems

The aim of this work was to study the self-assembly process of C3-symmetric molecules. To accomplish this objective 1,3,5 – benzentricarboxamides (BTA) derivatives were obtained. Five C3-symmetric molecules were synthesized in moderate to good yields (39-72%) using azo-benzene, aniline, benzylamine, tryptophan and tyrosine. The aggregation behavior of the BTA derivatives was probed with 1H-NMR spectroscopy, 1H-1H 2D Nuclear Overhauser Effect Spectroscopy (NOESY) and Diffusion Ordered Spectroscopy (DOSY). These experiments allowed to study the influence of H-bonding groups, aromatic rings, unsaturated bonds and the overall geometry in the molecular self-assembly associated with the different structural patterns present on these molecules. The stacking and large molecule behavior where observed in BTA 1, aniline derivative, BTA 4, tyrosine derivative or BTA 5, tryptophan derivative, with several of those discussed functional groups such as unsaturated bonds and H-bonding groups. BTA 5 was used in a few preliminary interaction studies with glucose and ammonium chloride showing interaction with the ammonium ion.

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.

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

IEEE CIRCUITS AND SYSTEMS MAGAZINE, Third Quarter

A coherent approach to non-integer order derivatives

Signal Processing, vol. 86, nº 10

A new least-squares approach to differintegration modeling

Signal Processing, Vol. 86, nº 10