An accurate approach based on the orthonormal shifted discrete Legendre polynomials for variable-order fractional Sobolev equation

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...

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 ...

Numerical Solution of Space-time Fractional two-dimensional Telegraph Equation by Shifted Legendre Operational Matrices

Fractional differential equations (FDEs) have attracted in the recent years a considerable interest due to their frequent appearance in various fields and their more accurate models of systems under consideration provided by fractional derivatives. For example, fractional derivatives have been used successfully to model frequency dependent damping behavior of many viscoelastic materials. They a...

Fractional differential equations with Legendre polynomials

Generalized Systolic Arrays for Discrete Transforms based on Orthonormal Polynomials

Many discrete transforms, such as the discrete cosine transform (DCT), are derived from sets of orthonormal polynomials. These sets of polynomials all possess recursion relationships, derived from a classic identity. In this paper, this recursion is used to derive generalized systolic arrays for the forward and inverse transform operations.