Regularity results for a class of nonlinear fractional Laplacian and singular problems

In this article, we investigate the existence, uniqueness, nonexistence, and regularity of weak solutions to nonlinear fractional elliptic problem type (P) (see below) involving singular nonlinearity weights in smooth bounded domain. We prove existence solution $$W_{loc}^{s,p}(\Omega )$$ via approximation method. Establishing a new comparison principle independent interest, uniqueness for $$0 \le \delta < 1+s- \frac{1}{p}$$ furthermore nonexistence $$\delta \ge sp.$$ Moreover, by virtue barrier arguments study behavior terms distance function. Consequently, Hölder up boundary optimal Sobolev solutions.