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.

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

Applied Mathematical Modelling, Vol.33

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 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

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

On the initial conditions in continuous-time fractional linear systems

Signal Processing, Vol. 83, nº 11

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

Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Overproduction, crystallization and preliminary X-ray characterization of Abn2, an endo-1,5-alpha-arabinanase from Bacillus subtilis.

Acta Crystallographica F64 (2008) 636-638

Fractional central differences and derivatives

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

Light controlled synthesis of nucleic acids

Dissertação apresentada para obtenção do grau de Doutor em Bioquímica - especialidade Biotecnologia, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Uma abordagem a sistemas de crescimento celular apical: síntese de um sensor para iões citosólicos de potássio

Dissertação para obtenção do Grau de Mestre em Bioorgânica