Jacobi polynomials method for a coupled system of Hadamard fractional Klein–Gordon–Schrödinger equations

In this work, the Caputo-type Hadamard fractional derivative is utilized to introduce a coupled system of time fractional Klein–Gordon-Schrödinger equations. The classical and shifted Jacobi polynomials are simultaneously applied to make a numerical technique for this system. To this aim, two operational matrices for the Caputo-type Hadamard fractional derivatives of the shifted Jacobi polynomials are gained. In the developed strategy, by considering a hybrid approximation of the problem's solution via the expressed polynomials and applying the obtained matrices, solving the original fractional system turns into solving an associated algebraic system of equations. Two test problems are examined to investigate the high accuracy of the developed procedure.