Scholars have put a lot of emphasis on time-varying linear matrix equations (LMEs) problems because of its importance in science and engineering. The problem of determining the time-varying LME’s minimum-norm least-squares solution (MLLE) is therefore tackled in this work. This is achieved by the use of NHZNN, a recently developed neutrosophic logic/fuzzy adaptive high-order zeroing neural network technique. The NHZNN is an advancement on the conventional zeroing neural network (ZNN) technique, which has shown great promise in solving time-varying tasks. To address the MLLE task for arbitrary-dimensional time-varying matrices, three novel ZNN models are presented. The models perform exceptionally well, as demonstrated by two simulation studies and two real-world applications to acoustic source tracking.