Generalized Solutions for Conformable Schrödinger Equation with Singular Potentials

This paper employs Colombeau algebra as a mathematical framework to establish both the existence and uniqueness of solutions for the fractional Schrödinger equation when subjected to singular potentials. A noteworthy contribution lies in the introduction of the concept of a generalized conformable semigroup, marking the first instance of its application. This innovative approach plays a pivotal role in demonstrating the sought-after results within the context of the fractional Schrödinger equation. The utilization of Colombeau algebra, coupled with the introduction of the generalized conformable semigroup, represents a novel and effective strategy for addressing challenges posed by singular potentials in the study of this particular type of Schrödinger equation.

کلیدواژه ها:

Conformable schrödinger equation ، Conformable derivative ، Generalized solution ، Conformable semigroup ، Singular potential