In this paper, using the monotone iterative technique, we discuss a new approximate method for solving multi-point boundary value problems of p-Laplacian fractional differential equations with singularities, which are of great importance in the fluid dynamics field. To do this, first, a sequence of auxiliary problems that release the nonlinear source terms contained in the equations from the singularities is set up, and the uniqueness and existence of their positive solutions are established. Next, we show the relative compactness of the sequence of unique solutions to these auxiliary problems to prove the solvability of our given problem. And we present some sufficient conditions to construct a sequence of approximate solutions that converges to an exact solution of our problem. Finally, we give two numerical examples to demonstrate our main results.

本文采用单调迭代技术，讨论了求解p的多点边值问题的一种新的近似方法。-具有奇异性的拉普拉斯分数阶微分方程，在流体动力学领域具有重要意义。为此，首先建立了一系列辅助问题，这些辅助问题从奇异性中释放出方程中包含的非线性源项，并确定了它们的正解的唯一性和存在性。接下来，我们展示了这些辅助问题的唯一解的序列的相对紧致性，以证明我们给定问题的可解性。并且我们提供了一些足够的条件来构造一系列收敛到我们问题的精确解的近似解。最后，我们给出两个数值示例来证明我们的主要结果。