A Fractal Dirac Eigenvalue Problem: Spectral Properties and Numerical Examples

F. Ayça Çetinkaya; Gage Plott

doi:10.5644/SJM.22.01.07

Authors

F. Ayça Çetinkaya University of Tennessee at Chattanooga, Department of Mathematics, Chattanooga, TN 37403, USA
Gage Plott University of Tennessee at Chattanooga, Department of Mathematics, Chattanooga, TN 37403, USA

DOI:

https://doi.org/10.5644/SJM.22.01.07

Keywords:

Fractal calculus, Fractal derivative, Dirac eigenvalue problem, Eigenvalues, Eigenfunctions

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 we present numerical examples to demonstrate the practical implications of our approach.

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