The aim of this research is to introduce a numerical technique relying on the shifted Jacobi polynomials (SJPs) and the Laplace transform (LT) for anatomizing a class of the fractional variational problems (FVPs). The derivative in this problem is in sense of the Caputo. To anatomizing FVP, first, we make an approximate for the Caputo operator Formula: see text using of the SJPs with unknown parameters. Then, applying LT, we access to Formula: see text and put in the study problem. The process of this method and the Lagrange multiplier method reduce the study problem to a system of nonlinear algebraic equations. In this body, unknown parameters calculate by solving the obtained system, and it gives Formula: see text. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme.
Sayevand et al. (Fri,) studied this question.