Generalized Solutions for Conformable Schrödinger Equations with Singular Potentials

Document Type : Research Paper

Authors

1 Laboratory of Applied Mathematics and Scientific Computing, Sultan Moulay Slimane University, PO Box 532, Beni Mellal, 23000, Morocco.

2 Department of Mathematics and Computer Science, Faculty of Sciences, PO Box 2121, Tetouan, Morocco.

Abstract

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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 05 July 2024

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History

  • Receive Date: 18 April 2023
  • Revise Date: 04 May 2024
  • Accept Date: 25 June 2024

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