The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces II

Abstract

In this work we study the Riemann-Liouville fractional integral of order α ∈ (0, 1/p) as an operator from L p (I; X) into L q (I; X), withwe prove an important property on the uniform continuity of this operator, regarding the order of integration, that allowed us to deduce necessary and sufficient conditions to ensure the compactness of the Riemann-Liouville fractional integral, which was an open problem.