Abstract In this manuscript, we extend our previous work on the Riemann-Liouville fractional integral of order > 0 α > 0 in Lᵖ (t₀, t₁;X) L p (t 0, t 1 ; X). In particular, we establish its boundedness for the case > 1/p α > 1 / p, with 1 1 p ∞, as well as the case >0 α > 0 with p = p = ∞. Moreover, we present a comprehensive summary of the results obtained so far.
Neto et al. (Wed,) studied this question.