A new least-squares approach to differintegration modeling

Signal Processing, Vol. 86, nº 10

Which differintegration?

IEE Proceedings Vision, Image & Signal Processing, vol. 152, nº 6

A signal processing view of differintegration

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

Which differintegration?

Despite the great advances in the theory and applications of fractional calculus, some topics remain unclear, making a systematic use difficult. In this paper, the fractional differintegration definition problem is studied from a systems point of view. Both local (Grunwald-Letnikov) and global (convolutional) definitions are considered. It is shown that the Cauchy formulation should be adopted since it is coherent with usual practice in signal processing and control applications.

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

Physics Letters A, vol. 372; Issue 7

A new symmetric fractional B-spline

Signal Processing, Vol. 83, nº 11

A new approach to the initial value problem

5th Portuguese Conference on Automatic Control, September, 5-7, 2002, Aveiro, Portugal

Time domain design of fractional differintegrators using least-squares

In this paper we propose the use of the least-squares based methods for obtaining digital rational approximations (IIR filters) to fractional-order integrators and differentiators of type sα, α∈R. Adoption of the Padé, Prony and Shanks techniques is suggested. These techniques are usually applied in the signal modeling of deterministic signals. These methods yield suboptimal solutions to the problem which only requires finding the solution of a set of linear equations. The results reveal that the least-squares approach gives similar or superior approximations in comparison with other widely used methods. Their effectiveness is illustrated, both in the time and frequency domains, as well in the fractional differintegration of some standard time domain functions.

A Fractional LC − RC Circuit

Mathematics Subject Classification: 26A33, 30B10, 33B15, 44A10, 47N70, 94C05

Some Fractional Extensions of the Temperature Field Problem in Oil Strata

This survey is devoted to some fractional extensions of the incomplete lumped formulation, the lumped formulation and the formulation of Lauwerier of the temperature field problem in oil strata. The method of integral transforms is used to solve the corresponding boundary value problems for the fractional heat equation. By using Caputo’s differintegration operator and the Laplace transform, new integral forms of the solutions are obtained. In each of the different cases the integrands are expressed in terms of a convolution of two special functions of Wright’s type.