Discrete delayed perturbation of Mittag-Leffler function and its application to linear fractional delayed difference system

The linear nonhomogeneous 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.