A Numerical Method for Solving Fractional Variational Problems by the Operational Matrix Based on Chelyshkov Polynomials

摘要

In this study, an accurate and effective method isproposed to solve fractional variational problems (FVPs).Fractional derivative is described in the sense of Caputo. In themethod, we simplify the fractional variational problems by theoperational matrices. The operational matrices are based on theChelyshkov polynomials. Using this method, the fractionalvariational problem can be transformed to a set of algebraicequations. And using the Lagranger multiplier technique, theunkown coefficients can be solved. The numerical solution ofFVPs is calculated by maple. Through different graphical andtables, the numerical results of illustrative evidence show thatthe method is reliable and powerful in solving fractionalvariational problems.