Analytical solution and stability of ψ-Prabhakar delayed systems: Application to antibiotic production

Authors

MUSTAFA AYDINFollow

Author ORCID Identifier

MUSTAFA AYDIN: 0000-0003-0132-9636

Abstract

The analytical solution of the linear ψ -Prabhakar delay differential equations is explored using the method of variation of parameters, in which a ψ -general delayed exponential matrix function is introduced. The ψ -Prabhakar calculus is enhanced in terms of the semi-group property, inversion results, and several simplified calculations and relations. The system's stability is analyzed within the framework of Ulam-Hyers stability. Finally, the theoretical findings are validated through an application to antibiotic production.

DOI

10.55730/1300-0098.3602

Keywords

ψ-Prabhakar derivative, time-delay, stability, Mittag-Leffler function, antibiotic production

First Page

472

Last Page

490

Publisher

The Scientific and Technological Research Council of Türkiye (TÜBİTAK)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

AYDIN, M (2025). Analytical solution and stability of ψ-Prabhakar delayed systems: Application to antibiotic production. Turkish Journal of Mathematics 49 (4): 472-490. https://doi.org/10.55730/1300-0098.3602