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

In this manuscript, we extend our previous work on the Riemann-Liouville fractional integral of order $$\alpha > 0$$ in $$L^p(t_0,t_1;X)$$ . In particular, we establish its boundedness for the case $$\alpha > 1/p$$ , with $$1< p < \infty $$ , as well as the case $$\alpha >0$$ with $$p = \infty $$ . Moreover, we present a comprehensive summary of the results obtained so far.