# Fractional heat equation

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The fractional heat equation refers to the parabolic equation $u_t + (-\Delta)^s u = 0,$ where $(-\Delta)^s$ stands for the fractional Laplacian.
In principle one could study the equation for any value of $s$. The values in the range $s \in (0,2]$ are particularly interesting because in that range the equation has a maximum principle.