Discrete Fractional Solutions of a Physical Differential Equation via $ \nabla $-DFC Operator

TL;DR

This paper introduces a novel discrete fractional calculus approach using the nabla operator to solve the radial Schr{"o}dinger equation, a physical differential equation with singularities, providing solutions with fractional forms involving discrete shift operators.

Contribution

The paper presents a new method applying the nabla discrete fractional operator to obtain solutions for the radial Schr{"o}dinger equation, extending fractional calculus techniques to singular physical equations.

Findings

Successful application of nabla discrete fractional operator to the radial Schr{"o}dinger equation.

Solutions obtained include fractional forms with discrete shift operator E.

Demonstrates effectiveness of discrete fractional calculus in solving singular differential equations.

Abstract

Discrete mathematics, the study of finite structures, is one of the fastest growing areas in mathematics and optimization. Discrete fractional calculus (DFC) theory that is an important subject of the fractional calculus includes the difference of fractional order. In present paper, we mention the radial Schr{\"o}dinger equation which is a physical and singular differential equation. And, we can obtain the particular solutions of this equation by applying nabla ($ \nabla $) discrete fractional operator. This operator gives successful results for the singular equations, and solutions have fractional forms including discrete shift operator $ E $.