Analysis and Investigation of fractional time Schrödinger equations

Abstract

In this paper , the time-fractional nonlinear Schrödinger differential equations are solved using Jacobi's space-time spectral coherence technique (JSC method) under suitable beginning and boundary conditions. The examined issue is first converted into a related system of single weak kernel non-linear integral partial differential equations with the definition and characteristics of integral and fractional derivative operators. Thus the issue reduces to a collection of nonlinear algebraic equations by integrating the system associated with integral differential equations in both spatial and temporal variables together with the approximation of the integral in the equation using Jacobi Gauss quadratic method. Several reliable iterative solutions may be used to solve the problem. Examining the suggested method's convergence, After the study's conclusion, we computed their soft L2 and soft L1 and gave a few numerical examples.