Aydın, M.2025-09-032025-09-0320251303-61491300-009810.55730/1300-0098.36022-s2.0-105016662903https://doi.org/10.55730/1300-0098.3602https://search.trdizin.gov.tr/en/yayin/detay/1336701/analytical-solution-and-stability-of-ps-prabhakar-delayed-systems-application-to-antibiotic-productionThe 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. © 2025 Elsevier B.V., All rights reserved.eninfo:eu-repo/semantics/openAccess26A3334A0834D2034KxxAntibiotic ProductionMittag-Leffler FunctionStabilityTime-DelayΨ-Prabhakar DerivativeArticle494Q2Q24724901336701WOS:001541678600006