Shifted Legendre polynomials algorithm used for the dynamic analysis of PMMA viscoelastic beam with an improved fractional model

the operational matrix of fractional integration for shifted legendre polynomials

in this article we implement an operational matrix of fractional integration for legendre polynomials. we proposed an algorithm to obtain an approximation solution for fractional differential equations, described in riemann-liouville sense, based on shifted legendre polynomials. this method was applied to solve linear multi-order fractional differential equation with initial conditions, and the...

Fractional differential equations with Legendre polynomials

New Operational Matrix For Shifted Legendre Polynomials and Fractional Differential Equations With Variable Coefficients

This paper is devoted to study a computation scheme to approximate solution of fractional differential equations(FDEs) and coupled system of FDEs with variable coefficients. We study some interesting properties of shifted Legendre polynomials and develop a new operational matrix. The new matrix is used along with some previously derived results to provide a theoretical treatment to approximate ...

fractional differential equations with legendre polynomials

Dynamic Response of an Axially Moving Viscoelastic Timoshenko Beam

In this paper, the dynamic response of an axially moving viscoelastic beam with simple supports is calculated analytically based on Timoshenko theory. The beam material property is separated to shear and bulk effects. It is assumed that the beam is incompressible in bulk and viscoelastic in shear, which obeys the standard linear model with the material time derivative. The axial speed is charac...