A Fractal Dirac Eigenvalue Problem: Spectral Properties and Numerical Examples

TL;DR

This paper investigates a Dirac boundary value problem involving a fractional derivative of order alpha, analyzing its spectral properties and providing numerical examples to illustrate practical applications.

Contribution

It introduces a spectral analysis of a Dirac problem with fractional derivatives and demonstrates numerical solutions, advancing understanding of fractional quantum systems.

Findings

Eigenvalues exhibit specific spectral distribution patterns.

Eigenfunctions possess unique fractional derivative properties.

Numerical examples validate theoretical spectral properties.

Abstract

In this paper, we study a Dirac boundary value problem where the operator is considered with a derivative of order $\alpha \in (0, 1]$, known as the $F^{\alpha}$-derivative. We prove some spectral properties of eigenvalues and eigenfunctions and present numerical examples to demonstrate the practical implications of our approach.