Aydın, MustafaMahmudov, Nazim Idrisoglu2025-09-302025-09-3020252221-95012218-681610.59849/2218-6816.2025.2.32-s2.0-105014111453https://doi.org/10.59849/2218-6816.2025.2.3https://hdl.handle.net/20.500.14720/28568The 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. © 2025 Elsevier B.V., All rights reserved.eninfo:eu-repo/semantics/closedAccessDiscrete Delayed PerturbationFractional DifferenceLinear SystemNabla Mittag-LefflerTime-DelayArticle152N/AQ2322