Existence of mild solutions for fractional Schrodinger equations in extended Colombeau algebras

The main crux of this research manuscript is to study the existence and uniqueness of generalized mild solutions for nonlinear Schrodinger equations with singular initial conditions in the extended algebras of generalized functions. The proofs are based on generalized semigroups theory and Gronwall's inequality. As an application, our theoretical results have been illustrated by providing a suitable example.

Keywords:

Extended Colombeau algebra , generalized mild solution , generalized function , Schr\"odinger equation