Linear subdiffusion in weighted fractional Hölder spaces

Abstract

<p style='text-indent:20px;'>For <inline-formula><tex-math id="M1">\begin{document}$ \nu\in(0,1) $\end{document}</tex-math></inline-formula>, we investigate the nonautonomous subdiffusion equation:</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \mathbf{D}_{t}^{\nu}u-\mathcal{L}u = f(x,t), $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where <inline-formula><tex-math id="M2">\begin{document}$ \mathbf{D}_{t}^{\nu} $\end{document}</tex-math></inline-formula> is the Caputofractional derivative and <inline-formula><tex-math id="M3">\begin{document}$ \mathcal{L} $\end{document}</tex-math></inline-formula> is a uniformly ellipticoperator with smooth coefficients depending on time. Undersuitable conditions on the given data and a minimal number (i.e.the necessary number) of compatibility conditions, the globalclassical solvability to the related initial-boundary valueproblems are established in the weighted fractional Hölderspaces.</p>