On the discrete delayed perturbation of Mittag-Leffler functions and their application to Caputo-type fractional difference equations

Abstract

The 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.