Numerical approximation of fractional variational problems with several dependent variables using Jacobi poly-fractonomials

We discuss a new numerical scheme using Jacobi poly-fractonomials for the fractional variational problem (FVP) with several dependent variables. The FVP is defined using the Caputo fractional derivative. Using Jacobi poly-fractonomials in the discussed method, the considered FVP is reduced to a system of algebraic equations. By solving this system of algebraic equations, an approximate solution of FVP is accomplished. We also proved the convergence of the presented scheme and the fractional variational error. At last, we perform some figurative examples to exhibit the legitimacy and pertinence of the current method.