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We study the controllability of the space-time fractional diffusion equation \\begin{equation*} \\begin{cases} \\mathbb D_t^\\alpha u+(-\\Delta)^su=0\\;\\;&\\mbox{ in }\\;(0,T)\\times\\Omega\\\\ u=g &\\mbox{ in }\\;(0,T)\\times(\\RR^N\\setminus\\Omega)\\\\ u(0,\\cdot)=u_0&\\mbox{ in }\\;\\Omega, \\end{cases} \\end{equation*} where $u=u(t,x)$ is the state to be controlled and $g=g(t,x)$ is the control function which is localized in a subset $\\mathcal O$ of $\\Omc$. Here, $0<\\alpha\\le 1$, $0<s<1$ and $T>0$ be real numbers. 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We study the controllability of the space-time fractional diffusion equation \\begin{equation*} \\begin{cases} \\mathbb D_t^\\alpha u+(-\\Delta)^su=0\\;\\;&\\mbox{ in }\\;(0,T)\\times\\Omega\\\\ u=g &\\mbox{ in }\\;(0,T)\\times(\\RR^N\\setminus\\Omega)\\\\ u(0,\\cdot)=u_0&\\mbox{ in }\\;\\Omega, \\end{cases} \\end{equation*} where $u=u(t,x)$ is the state to be controlled and $g=g(t,x)$ is the control function which is localized in a subset $\\mathcal O$ of $\\Omc$. Here, $0<\\alpha\\le 1$, $0<s<1$ and $T>0$ be real numbers. 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