Shrinking targets for non-autonomous dynamical systems corresponding to Cantor series expansions

We provide a closed formula of Bowen type for the Hausdorff dimension of a very general shrinking target scheme generated by the non-autonomous dynamical system on the interval $[0,1)$, viewed as $\mathbb{R}/\mathbb{Z}$, corresponding to a given method of Cantor series expansion. We also examine a wide class of examples utilizing our theorem. In particular, we provide a Diophantine approximation interpretation of our scheme.