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In this paper we study positive solutions to problem involving the fractionalLaplacian $(E)$ $(-\Delta)^{\alpha} u(x)+|u|^{p-1}u(x)=0 inx\in\Omega\setminus\mathcal{C}$, subject to the conditions $u(x)=0$$x\in\Omega^c$ and $\lim_{x\in\Omega\setminus\mathcal{C},x\to\mathcal{C}}u(x)=+\infty$, where $p>1$ and $\Omega$ is an open bounded$C^2$ domain in $\mathbb{R}^N$, $\mathcal{C}\subset \Omega$ is a compact $C^2$manifold with $N-1$ multiples dimensions and without boundary, the operator$(-\Delta)^{\alpha}$ with $\alpha\in(0,1)$ is the fractional Laplacian.  We consider the existence of positive solutions for problem $(E)$. Moreover,we further analyze uniqueness, asymptotic behaviour and nonexistence.

Self-generated interior blow-up solutions in fractional elliptic equation with absorption