Stability and convergence of the space fractional variable-order Schrödinger equation

The space fractional Schrdinger equation was further extended to the concept of space fractional variable-order derivative. The generalized equation is very difficult to handle analytically. We solved the generalized equation numerically via the Crank-Nicholson scheme. The stability and the convergence of the space fractional variable-order Schrdinger equation were presented in detail.