On a $\psi$-fractional Dirac equation

Bilender P. Allahverdiev^ab, Hüseyin Tuna<sup>cb

a</sup> Khazar University, Baku, Azerbaijan
^b Research Center of Econophysics, UNEC-Azerbaijan State University of Economics, Baku, Azerbaijan
^c Faculty of Arts and Sciences, Mehmet Akif Ersoy University, Burdur, Turkey

Abstract: In this study, we use the $\psi$-Riemann-Liouville and $\psi$-Caputo derivatives to construct a $\psi$-fractional Dirac system$.$ Several characteristics of this system were examined. Lastly, an adequate eigenvalue condition is provided for the uniqueness and existence of the corresponding eigenfunctions.

Keywords: Dirac system, Hilfer derivatives, eigenvalues, eigenfunctions.

UDC: 517.9

Received: 10.06.2025
Received in revised form: 18.07.2025
Accepted: 14.09.2025

Language: English