A renovated Buongiorno's model with fractional differential equation is proposed to investigate the heat and mass transfer characteristics of Sisko nanofluid over a continuously moving flat plate. The fractional Cattaneo heat flux is introduced to describe the anomalous heat transport of Sisko nanofluid considering the influences of Brownian diffusion and thermophoresis. The governing boundary layer equations of continuity, momentum, energy and concentration are reduced by dimensionless variable and solved numerically. The quantities of physical interest are graphically presented and discussed in detail. It is found that the renovated model with Caputo time fractional derivatives is more capable to explain the abnormal thermal conductivity enhancement, which is also able to describe the influence of memory on the nanofluid behavior. Results indicate that the heat and mass transfer ability of Sisko nanofluid is reduced by the temperature fractional derivative parameter in both cases of shear thinning and shear thickening. Moreover, the rise of temperature fractional derivative parameter results in a significant increase of the average Nusselt number and a slight decrease of the average Sherwood number. (C) 2018 Elsevier Ltd. All rights reserved.