  The aim goal of this paper is to treat the following problem
\begin{equation*} \left\{ \begin{array}{rcll} u_t+(-\D^s_{p}) u &=&\dyle \l
\dfrac{u^{p-1}}{|x|^{ps}} & \text{ in } \O_{T}=\Omega \times (0,T), \\ u&\ge &
0 & \text{ in }\ren \times (0,T), \\ u &=& 0 & \text{ in }(\ren\setminus\O)
\times (0,T), \\ u(x,0)&=& u_0(x)& \mbox{ in }\O, \end{array}% \right.
\end{equation*} where $\Omega$ is a bounded domain containing the origin, $$
(-\D^s_{p})\, u(x,t):=P.V\int_{\ren}
\,\dfrac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+ps}} \,dy$$ with
$1<p<N, s\in (0,1)$ and $f, u_0$ are non negative functions. The main goal of
this work is to discuss the existence of solution according to the values of
$p$ and $\l$.
