Fractional order of Legendre-type matrix polynomials

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

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 ...

Numerical Calculation of Fractional Derivatives for the Sinc Functions via Legendre Polynomials

‎This paper provides the fractional derivatives of‎ ‎the Caputo type for the sinc functions‎. ‎It allows to use efficient‎ ‎numerical method for solving fractional differential equations‎. ‎At‎ ‎first‎, ‎some properties of the sinc functions and Legendre‎ ‎polynomials required for our subsequent development are given‎. ‎Then‎ ‎we use the Legendre polynomials to approximate the fractional‎ ‎deri...