Aydin, M.Mahmudov, N. I.2025-09-302025-09-3020252218-681610.59849/2218-6816.2025.2.32-s2.0-105014111453https://doi.org/10.59849/2218-6816.2025.2.3The linear nonhomogeneous fractional difference system with constant coefficients is introduced. An explicit solution to this system is obtained by proposing a newly discrete retarded perturbation of the nabla Mittag-Leffler-type function containing matrix equations that provide non-permutability. A couple of special cases obtained from our results are discussed.eninfo:eu-repo/semantics/openAccessDiscrete Delayed PerturbationFractional DifferenceNabla Mittag–LefflerLinear SystemTime DelayArticle152N/AQ2322WOS:001560795700001