Sequential fractional calculus between Banach spaces and alternative Ostrowski and Grüss type inequalities

Abstract

In this article, we present a sequential fractional calculus of Caputo type for functions between Banach spaces. Left and right fractional derivatives are defined on a segment of a Banach space, then we develop our theory. We apply the above to new alternative Ostrowski and Grüss type inequalities at a very abstract level.