Aydın, Mustafa2025-09-032025-09-0320251300-00981303-614910.55730/1300-0098.3602https://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.eninfo:eu-repo/semantics/openAccessPsi-Prabhakar DerivativeTime-DelayStabilityMittag-Leffler FunctionAntibiotic ProductionArticle494Q2Q24724901336701WOS:001541678600006