The Riemann-Liouville fractional integral in Bochner-Lebesgue spaces I
نویسندگان
چکیده
<p style='text-indent:20px;'>In this paper we study the Riemann-Liouville fractional integral of order <inline-formula><tex-math id="M1">\begin{document}$ \alpha&gt;0 $\end{document}</tex-math></inline-formula> as a linear operator from id="M2">\begin{document}$ L^p(I,X) into itself, when id="M3">\begin{document}$ 1\leq p\leq \infty $\end{document}</tex-math></inline-formula>, id="M4">\begin{document}$ I=[t_0,t_1] (or id="M5">\begin{document}$ I=[t_0,\infty) $\end{document}</tex-math></inline-formula>) and id="M6">\begin{document}$ X is Banach space. In particular, id="M7">\begin{document}$ obtain necessary sufficient conditions to ensure its compactness. We also prove that defines id="M8">\begin{document}$ C_0- $\end{document}</tex-math></inline-formula>semigroup but does not uniformly continuous semigroup. close by presenting lower higher bounds norm operator.</p>
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ژورنال
عنوان ژورنال: Communications on Pure and Applied Analysis
سال: 2022
ISSN: ['1534-0392', '1553-5258']
DOI: https://doi.org/10.3934/cpaa.2022118