An Accurate Ritz Approximation Scheme for Tempered Fractional Variational Models

Abstract This work presents a numerical approach for solving the tempered fractional variational problems (TFVPs). The exact solution is approximated using an expansion based on tempered Jacobi poly-fractonomials (TJFs), which are taken as the basis function. By employing the Rayleigh-Ritz technique, the original TFVPs are transformed into a corresponding system of algebraic equations. A comprehensive convergence study and error estimation are provided to assess the theoretical performance of the method. Furthermore, to validate the accuracy of our proposed method, we present numerical examples that demonstrate how the errors decay exponentially.