ON ANATOMIZING A CLASS OF THE FRACTIONAL VARIATIONAL PROBLEMS WITH THE LAGRANGE MULTIPLIER

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 the sense of the Caputo. To anatomizing FVP, first, we make an approximation for the Caputo operator ([Formula: see text]) using the SJPs with unknown parameters. Then, applying LT, we access [Formula: see text] and put it in the study problem. The process of this method and the Lagrange multiplier method reduces the study problem to a system of nonlinear algebraic equations. In this system, unknown parameters are calculated 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.