This paper studies a class of fourth point singular boundary value problem of $ p $-Laplacian operator in the setting of a specific kind of conformable derivatives. By using the upper and lower solutions method and fixed point theorems on cones., necessary and sufficient conditions for the existence of positive solutions are obtained. In addition, we investigate the dependence of the solution on the order of the conformable differential equation and on the initial conditions.

中文翻译：

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非线性奇异\begin{document}$ p $\end{document} -一致导数框架中的拉普拉斯边值问题

本文研究了一类特殊的可合导数设置下$p$-Laplacian算子的一类四点奇异边值问题。利用上下解法和圆锥上的不动点定理，得到了正解存在的充要条件。此外，我们研究了解对一致微分方程阶数和初始条件的依赖性。