An efficient discrete Chebyshev polynomials strategy for tempered time fractional nonlinear Schrödinger problems

The tempered fractional derivative in the Caputo form is utilized to define the time fractional nonlinear Schrödinger equation and a coupled system of nonlinear Schrödinger equations. The ODCPs are used to design a numerical strategy for these problems. To this purpose, some operational matrices for these polynomials are obtained. In the designed procedures, the problem's solution are obtained by solving an algebraic system of equations. These systems are obtained by approximating the solution with the ODCPs and employing the expressed matrix relationships, along with the collocation technique. Some examples are presented to check the validity of the developed algorithms. The reported results acknowledged the high accuracy of the designed schemes.