Aydin, MustafaMahmudov, Nazim2025-09-032025-09-0320250971-36112367-250110.1007/s41478-025-00954-12-s2.0-105013165836https://doi.org/10.1007/s41478-025-00954-1https://hdl.handle.net/20.500.14720/28329The linear nonhomogeneous Caputo-type fractional difference system with constant coefficients is introduced. An explicit solution to the system is acquired by proposing a newly discrete retarded perturbation of the nabla Mittag-Leffer-type function containing such matrix equations that provide non-permutability. A couple of special cases obtained from our results are discussed.eninfo:eu-repo/semantics/closedAccessDiscrete Delayed PerturbationFractional DifferenceNabla Mittag-LefflerLinear SystemTime-Delay34Kxx39AxxArticleN/AQ3WOS:001550326200001