In this paper, we focus on the existence of positive solutions for a class of weakly singular Hadamard-type fractional mixed periodic boundary value problems with a changing-sign singular perturbation. By using nonlinear analysis methods combining with some numerical techniques, we further discuss the effect of the perturbed term for the existence of solutions of the problem under the positive, negative, and changing-sign cases. The interesting points are that the nonlinearity can be singular at the second and third variables and be changing-sign.

中文翻译：

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具有变化符号非线性的弱奇异Hadamard型分数阶微分方程的正解

在本文中，我们集中于一类带有变化符号奇摄动的弱奇异Hadamard型分数混合周期边值问题的正解的存在。通过使用非线性分析方法并结合一些数值技术，我们进一步讨论了扰动项对正，负和变号情况下问题解的存在的影响。有趣的是，非线性在第二和第三变量处可以是奇异的，并且可以是正负号。