Tempered fractional derivatives originated from the tempered fractional diffusion equations (TFDEs) modeled on the whole space R (see [?]). For numerically solving TFDEs, two kinds of generalized Laguerre functions were defined and some important properties were proposed to establish the approximate theory. The related prototype tempered fractional differential problems was proposed and solved ...

In this paper, a new LQG control design based on input-output data for linear time invariant continuous-time systems is proposed. Considering the laguerre series expansion of input-output signals, the controller can be synthesized using only the coefficients by an algebraic calculation. The analysis of the system transformed by the laguerre series expansion is utilized to lead this design metho...

The Encyclopedia of Integer Sequences includes some sequences that are connected with the Bell numbers and that have a particular combinatorial meaning. In this article, we find a general meaning for framing sequences, including the above mentioned ones. Furthermore, by using Laguerre-type derivatives, we derive the Laguerre-type Bell numbers of higher order, showing, as a by-product, that it i...

In this paper, ‎the multi-sensor fault diagnosis in the exhaust temperature sensors of a V94.2 heavy duty gas turbine is presented‎. ‎A Laguerre network-based fuzzy modeling approach is presented to predict the output temperature of the gas turbine for sensor fault diagnosis‎. Due to the nonlinear dynamics of the gas turbine, in these models the Laguerre filter parts are related to the linear d...

In this paper, we use a digital laser to generate high-radial-order Laguerre-Gaussian, LGp,0 modes by loading digital holograms on a phase-only spatial light modulator that act as an end mirror of a diode-end-pumped laser resonator. The digital holograms were encoded with an amplitude ring mask, which contained absorption rings that match the p-zeros of the Laguerre polynomial. We demonstrate t...

Protein structures are an ensemble of atoms determined experimentally mostly by X-ray crystallography or Nuclear Magnetic Resonance. Studying 3D protein structures is a key point for better understanding protein function at a molecular level. We propose a set of accurate tools, for analysing protein structures, based on the reliable method of Voronoi-Laguerre tessellations. The Voronoi Laguerre...

The Fourier transforms of Laguerre functions play the same canonical role in wavelet analysis as do the Hermite functions in Gabor analysis. We will use them as analyzing wavelets in a similar way the Hermite functions were recently by Gröchenig and Lyubarskii in Gabor frames with Hermite functions, C. R. Acad. Sci. Paris, Ser. I 344 157-162 (2007). Building on Seip ́s work Beurling type density...