Demonstrates boundedness of the Riemann-Liouville fractional integral in Bochner-Lebesgue spaces, suggesting important implications for mathematical analysis.
In this manuscript, we extend our previous work on the Riemann-Liouville fractional integral of order α > 0 α > 0 in Lᵖ(t₀,t₁;X) L p ( t 0 , t 1 ; X ) . In particular, we establish its boundedness for the case α > 1/p α > 1 / p , with 1< p < ∞ 1 < p < ∞ , as well as the case α >0 α > 0 with p = ∞ p = ∞ . Moreover, we present a comprehensive summary of the results obtained so far.
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Neto et al. (2026) studied this question.
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