In this paper, we construct a new hierarchy based on the third q-discrete Painlevé equation (qP_III) and also study the hierarchy of the second q-discrete Painlevé equation (qP_II). Both hierarchies are derived by using reductions of the general lattice modified Korteweg-de Vries equation. Our results include Lax pairs for both hierarchies and these turn out to be higher degree expansions of the non-resonant ones found by Joshi and Nakazono [29] for the second-order cases. We also obtain Bäcklund transformations for these hierarchies. Special q-rational solutions of the hierarchies are constructed and corresponding q-gamma functions that solve the associated linear problems are derived.

在本文中，我们基于第三个q离散Painlevé方程（q P _III）构造了一个新的层次结构，并研究了第二个q离散Painlevé方程（q P _II）的层次结构。这两个层次结构都是通过使用一般晶格修饰的Korteweg-de Vries方程的约简得出的。我们的结果包括两个层次的Lax对，结果证明是Joshi和Nakazono [29]在二阶情况下发现的非共振对的高次扩展。我们还获得了这些层次结构的Bäcklund转换。构造层次的特殊q-有理解并对应q导出了解决相关线性问题的-gamma函数。