Application of the Rayleigh-Ritz method to solve a class of fractional variational problem

Abstract

The aim of this paper is to investigate a direct numerical method for solving a class of a fractional variational problem (FVP). The fractional derivative in the FVP is in the Caputo sense. The Rayleigh-Ritz method is introduced for the numerical solution of the FVP. The corresponding Euler-Lagrange equation contain the left and right Caputo fractional derivatives. We approximate the solution of the FVP by using the trigonometric function. Finally, the illustrative example is presented.

The Laplace‐collocation method for solving fractional differential equations and a class of fractional optimal control problems

“…This calculus is used to obtain exact solutions of an initial value problem for linear FDEs with constant coefficients and fractional derivatives in Caputo's sense. In the work of Błaszczyk, a scheme based on the variational Rayleigh‐Ritz method was proposed to obtain a numerical solution of the fractional oscillator equation. Yan and et al introduced higher‐order numerical methods for solving FDEs.…”