Numerical solution of time fractional nonlinear Schrödinger equation arising in quantum mechanics by cubic B-spline finite elements

In the present article, we are going to investigate the numerical solutions of time fractional nonlinear Schrödinger equation which is frequently encountered in quantum mechanics by using cubic B-spline collocation method. To be able to control the efficiency of the proposed method, some sample problems have been studied in this article. The outstanding purpose of the paper is to indicate that the finite element method based on the cubic B-spline collocation method approach can also be suitable for the handling of the fractional differential equations. At the end, the results of numerical experiments are compared with those of analytical solution to ensure the accuracy and efficiency of the presented scheme.