ℓp-Maximal Regularity for a Class of Fractional Difference Equations on Umd Spaces: The Case 1 ≪ α ≤ 2

By using Blunck s operator-valued Fourier multiplier theorem, we completely characterize the existence and uniqueness of solutions in Lebesgue sequence spaces for a discrete version of the Cauchy problem with fractional order 1 < α ≤ 2. This characterization is given solely in spectral terms on the data of the problem, whenever the underlying Banach space belongs to the UMD-class. © 2017 by the Tusi Mathematical Research Group.