Application of Fixed Point Theorem for Stability Analysis of a Nonlinear Schrodinger with Caputo-Liouville Derivative

Abstract

Using the new Caputo-Liouville derivative with fractional order, we have modified the nonlinear Schrdinger equation. We have shown some useful in connection of the new derivative with fractional order. We used an iterative approach to derive an approximate solution of the modified equation. We have established the stability of the iteration scheme using the fixed point theorem. We have in addition presented in detail the uniqueness of the special solution.