Title: Sobolev Regularity Theory for Time-Fractional Evolution Equations with Anisotropic Diffusion

Speaker: Jae-Hwan Choi (KIAS)

Abstract: In this talk, we develop a Sobolev space framework for time-space nonlocal evolution equations arising from fractional kinetics. The nonlocality in time is captured by the Caputo fractional derivative, while the spatial operator is given by the infinitesimal generator of a vector of independent subordinate Brownian motions, leading to anisotropic diffusion. These equations naturally appear in various applied contexts, and our approach provides a rigorous analytic foundation for their study.