摘要：We prove the nonexistence of solutions of the fractional diffusion equation with time-space nonlocal source $$\begin{aligned} u_{t} + (-\Delta )^{\frac{\beta }{2}} u =\bigl(1+ \vert x \vert \bigr)^{ \gamma } \int _{0}^{t} (t-s)^{\alpha -1} \vert u \vert ^{p} \bigl\Vert \nu ^{ \frac{1}{q}}(x) u \bigr\Vert _{q}^{r} \,ds \end{aligned}$$ for $(x,t) \in \mathbb{R}^{N}\times (0,\infty )$ with initial data $u(x,0)=u_{0}(x) \in L^{1}_{\mathrm{loc}}(\mathbb{R}^{N})$ , where $p,q,r>1$ , $q(p+r)>q+r$ , $0<\gamma \leq 2 $ , $0<\alpha <1$ , $0<\beta \leq 2$ , $(-\Delta )^{\frac{\beta }{2}}$ stands for the fractional Laplacian operator of order β, the weight function $\nu (x)$ is positive and singular at the origin, and $\Vert \cdot \Vert _{q}$ is the norm of $L^{q}$ space.
