The present investigation analyzes the efficacy of differential transform methods (DTM) for hydrodynamically fully developed purely electroosmotically actuated flow of pseudoplastic fluids inside a microchannel. Expressions are mathematically deduced for non-dimensional velocity field and flow rate through both analytical and differential transform methods (DTM) and the effectiveness of the latter for flow rate has been obtained by maximum relative percentage deviation. Critical values of the transverse location in the microchannel are noted beyond which the magnitude of velocity changes its trend with thickness of the electrical double layer near the microchannel wall. Implementation of DTM is found to be highly stable, consistent and convergent for higher values of flow behavior index. Critical values of Debye–Hückel parameter are noted beyond which there is a significant deviation of DTM solutions from analytical ones. The dimensionless flow rate obtained by DTM is observed to converge faster for higher values of flow behavior index.