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In this paper, we first establish Hopf's lemmas for parabolic fractional <tex-math id="M1">{document}p{document}</tex-math>-equations for <tex-math id="M2">{document}p ≥ 2{document}</tex-math>. Then we derive an asymptotic Hopf's lemma for anti-symmetric solutions to parabolic fractional Laplacians. We believe that these Hopf's lemmas will become powerful tools in obtaining qualitative properties of solutions for nonlocal parabolic equations.
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Wang et al. (2022) studied this question.
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