\begin{document}$\ell_*$\end{document} influences the size of the black hole shadow in two ways and modifies the weak deflection angle. Constraints on \begin{document}$\ell_*$\end{document} are derived from the EHT observations, showing significant deviations from standard Schwarzschild black hole predictions, which range from \begin{document}$10^{9}$\end{document} to \begin{document}$10^{10}$\end{document} orders of magnitude. Additionally, the weak deflection angle is computed using the non-asymptotic generalization of the Gauss-Bonnet theorem (GBT) to reveal the effects of finite-distance and multi-scale parameters. Using the Sun in the Solar System test, we observe that the constraints for \begin{document}$\ell_*$\end{document} range from \begin{document}$10^{8}$\end{document} to \begin{document}$10^{9}$\end{document}orders of magnitude. Results from the weighted derivative formalism generate a dS/AdS-like behavior, where smaller deviations are found in the strong field regime than in the weak field regime. The results suggest that, while these effects are subtle, they provide a potential observational signature of quantum gravity effects. The findings presented here contribute to the broader effort of testing alternative theories of gravity through black hole observations, offering a new perspective on the quantum structure of spacetime at cosmological and astrophysical scales."> Traces of quantum fuzziness on the black hole shadow and particle deflection in the multi-fractional theory of gravity -
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