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 Bochner-Lebesgue spaces. We specifically address the remaining cases concerning its boundedness when $\alpha >1\mathrm{/}p$. Furthermore, we extend some of our previous results by investigating some non-standard function spaces. Finally, we provide a comprehensive summary of the obtained results.