A semilinear problem associated to the space-time fractional heat equation in ${\mathbb{R}}^N$

Carmen Cortázar, Fernando Quirós, Noemí Wolanski

We study the fully nonlocal semilinear equation ${\partial }_t^{\alpha }u+(-\Delta {)}^{\beta }u=|u{|}^{p-1}u$, $p\ge 1$, where ${\partial }_t^{\alpha }$ stands for the Caputo derivative of order $\alpha \in (0,1)$ and $(-Δ)^β…