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In particular, we consider the problem $$(P_\\theta)\\quad \\left\\{ \\begin{array}{rcl} u_t+(-\\Delta)^{s} u&=&\\l\\dfrac{\\,u}{|x|^{2s}}+\\theta u^p+ c f\\mbox{ in } \\Omega\\times (0,T),\\\\ u(x,t)&>&0\\inn \\Omega\\times (0,T),\\\\ u(x,t)&=&0\\inn (\\ren\\setminus\\Omega)\\times[ 0,T),\\\\ u(x,0)&=&u_0(x) \\mbox{ if }x\\in\\O, \\end{array} \\right. $$ where $N> 2s$, $0<s<1$, $(-\\Delta)^s$ is the fractional Laplacian of order $2s$, $p>1$, $c,\\l>0$, $u_0\\ge 0$, $f\\ge 0$ are in a suitable class of functions and $\\theta=\\{0,1\\}$. 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