Some general results on fractional Banach sets

Abstract

The gamma function which is expressed by an improper integral is used to establish the fractional differenceoperators and fractional Banach sets. In this study, we achieve some comprehensive and complementary results relatedto characterizations of the matrix classes of fractional Banach sets. We also obtain some identities or inequalities for theHausdorff measure of noncompactness of the corresponding matrix operators, and finally find the necessary and sufficientconditions for those matrix operators to be compact.