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The linear nonhomogeneous fractional difference system with constantcoefficients is introduced. An explicit solution to the system is acquired byproposing a newly discrete retarded perturbation of the nablaMittag-Leffer-type function containing such matrix equations that providenon-permutability. A couple of special cases obtained from our results arediscussed.

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