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In this article, we consider the space-time Fractional (nonlocal) diffusion equation $$\partial_t^\beta u(t,x)={\mathtt{L}_D^{\alpha_1,\alpha_2}} u(t,x), \ \ t\geq 0, \ x\in D, $$ where $\partial_t^\beta$ is the Caputo fractional derivative of order $\beta \in (0,1)$ and the differential operator ${\mathtt{L}_D^{\alpha_1,\alpha_2}}$ is the generator of a L\'evy process, sum of two symmetric independent $\alpha_1-$stable and $\alpha_2-$stable processes and ${D}$ is the open unit interval in $\mathbb{R}$.
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