Aydin, Mustafa2026-01-302026-01-3020260170-42141099-147610.1002/mma.704992-s2.0-105027778428https://doi.org/10.1002/mma.70499https://hdl.handle.net/20.500.14720/29654In this paper, we define a general delayed perturbation of the three-parameter Mittag-Leffler type matrix function, which can be seen as a generalization of both the delayed perturbation of the two-parameter Mittag-Leffler type function and the delayed perturbation of the three-parameter Mittag-Leffler type function. We examine a couple of its properties in addition to identifying some of its relations with the existing Mittag-Leffler-type functions in the literature. We present an explicit formula by constructing on the general delayed perturbation of the three-parameter Mittag-Leffler type function as a solution to a linear fractional differential delayed equation with two distinct approaches.eninfo:eu-repo/semantics/closedAccessFractional Linear EquationGeneral Delay PerturbationMittag-Leffler FunctionPrabhakar Fractional DerivativeRepresentation of SolutionsArticle