On a generalized Laguerre operational matrix of fractional integration

A new operationalmatrix of fractional integration of arbitrary order for generalized Laguerre polynomials is derived.The fractional integration is described in the Riemann-Liouville sense.This operational matrix is applied together with generalized Laguerre tau method for solving general linearmultitermfractional differential equations (FDEs).Themethod has the advantage of obtaining the solution in terms of the generalized Laguerre parameter. In addition, only a small dimension of generalized Laguerre operational matrix is needed to obtain a satisfactory result. Illustrative examples reveal that the proposedmethod is very effective and convenient for linear multiterm FDEs on a semi-infinite interval.

Operational modal monitoring of ancient structures using wireless technology

Operational Modal Analysis is currently applied in structural dynamic monitoring studies using conventional wired based sensors and data acquisition platforms. This approach, however, becomes inadequate in cases where the tests are performed in ancient structures with esthetic concerns or in others, where the use of wires greatly impacts the monitoring system cost and creates difficulties in the maintenance and deployment of data acquisition platforms. In these cases, the use of sensor platforms based on wireless and MEMS would clearly benefit these applications. This work presents a first attempt to apply this wireless technology to the structural monitoring of historical masonry constructions in the context of operational modal analysis. Commercial WSN platforms were used to study one laboratory specimen and one of the structural elements of a XV century building in Portugal. Results showed that in comparison to the conventional wired sensors, wireless platforms have poor performance in respect to the acceleration time series recorded and the detection of modal shapes. However, for frequency detection issues, reliable results were obtained, especially when random excitation was used as noise source.

A Review of Operational Matrices and Spectral Techniques for Fractional Calculus

Recently, operational matrices were adapted for solving several kinds of fractional differential equations (FDEs). The use of numerical techniques in conjunction with operational matrices of some orthogonal polynomials, for the solution of FDEs on finite and infinite intervals, produced highly accurate solutions for such equations. This article discusses spectral techniques based on operational matrices of fractional derivatives and integrals for solving several kinds of linear and nonlinear FDEs. More precisely, we present the operational matrices of fractional derivatives and integrals, for several polynomials on bounded domains, such as the Legendre, Chebyshev, Jacobi and Bernstein polynomials, and we use them with different spectral techniques for solving the aforementioned equations on bounded domains. The operational matrices of fractional derivatives and integrals are also presented for orthogonal Laguerre and modified generalized Laguerre polynomials, and their use with numerical techniques for solving FDEs on a semi-infinite interval is discussed. Several examples are presented to illustrate the numerical and theoretical properties of various spectral techniques for solving FDEs on finite and semi-infinite intervals.