Lp-Maximal Regularity for Fractional Difference Equations on Umd Spaces

Let T be a bounded linear operator defined on a U M D Banach space X. We introduce an operator theoretical method for linear fractional difference equations based on the notion of α-resolvent sequence of bounded and linear operators. Then, we define and characterize the lp - maximal regularity of solutions for the problem (Formula presented.) solely in terms of the R-boundedness of the set (Formula presented.) © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim