In this paper, we consider the existence of positive solutions for a Hadamard-type fractional differential equation with singular nonlinearity. By using the spectral construct analysis for the corresponding linear operator and calculating the fixed point index of the nonlinear operator, the criteria of the existence of positive solutions for equation considered are established. The interesting point is that the nonlinear term possesses singularity at the time and space variables.

中文翻译：

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谱构造分析法解奇异的Hadamard型分数阶微分方程

在本文中，我们考虑了具有奇异非线性的Hadamard型分数阶微分方程的正解的存在性。通过对相应的线性算子进行频谱构造分析并计算非线性算子的不动点指数，建立了所考虑方程正解存在性的标准。有趣的一点是，非线性项在时空变量中具有奇异性。