Existence and estimates of positive solutions for some singular fractional boundary value problems (Q1722117)

Summary: We establish the existence and uniqueness of a positive solution \(u\) for the following fractional boundary value problem: \(\mathrm{:D}^\alpha u(x) = - a(x) u^\sigma(x)\), \(x \in(0, 1)\) with the conditions \(\lim_{x \rightarrow 0^+}\) \(x^{2 - \alpha} u(x) = 0\), \(u(1) = 0\), where \(1 < \alpha \leq 2\), \(\sigma \in(- 1, 1)\), and \(a\) is a nonnegative continuous function on \((0, 1)\) that may be singular at \(x = 0\) or \(x = 1\). We also give the global behavior of such a solution.