Numerical treatment of the strongly coupled nonlinear fractal-fractional Schrödinger equations through the shifted Chebyshev cardinal functions

In this paper, a new version of the strongly coupled nonlinear fractal-fractional Schrödinger equations is introduced by using the fractal-fractional derivatives in the Riemann-Liouville sense with Mittag-Leffler kernel. An accurate operational matrix method based on the shifted Chebyshev cardinal functions is established for solving this new class of problems. Along the way, a new operational matrix of fractal-fractional derivative is derived for these basis functions. The main characteristic of the proposed method is that it transforms solving the original problem to an algebraic system of equations by exploiting the operational matrix techniques.