Aydin, M.Mahmudov, N. I.2025-06-012025-06-0120252076-25852219-125910.30546/2219-1259.16.1.2025.115https://doi.org/10.30546/2219-1259.16.1.2025.115https://hdl.handle.net/20.500.14720/24990The representation of an explicit solution to the Prabhakar fractional differential delayed system is studied employing the far-famed Laplace transform technique. Second, the existence uniqueness of the solution is debated together with the Ulam-Hyers stability of a semilinear Prabhakar fractional differential delayed system. Thirdly, the necessary and sufficient circumstances for the controllability of linear Prabhakar fractional differential delayed system are determined by describing the Gramian matrix. A sufficient circumstance for the relative controllability of a semilinear Prabhakar fractional differential delayed system is studied via the Krasnoselskii's fixed point theorem. Numerical examples are offered to verify the theoretical findings.eninfo:eu-repo/semantics/openAccessPrabhakar Fractional DerivativeDifferential Delayed EquationExistence UniquenessStability And ControllabilityMittag-Leffler FunctionArticle161Q1N/A115136WOS:001484647900008