Fractional Order Continuity and Some Properties about Integrability and Differentiability of Real Functions

Abstract

In this paper a certain function spaceCα, 0≤α≤1, larger than the space of continuous functions, is introduced in order to study new properties and the extension of some already known results about the Riemann-Liouville fractional integral and derivative operators. Sufficient conditions for the continuity ofI1-αafare given. Furthermore, necessary conditions are given for the pointwise existence of fractional derivatives. The existence of a derivative of order β, from the existence of a certain derivative of order α, β