The aim of this study is to investigate the influence of carbon nanotubes (CNTs) nanofluid on natural convection with Prabhakar-like thermal transport, near an infinite vertical heated plate. The generalized memory effect is described by the time-fractional Prabhakar derivative. Nanofluid flow features such as velocity and temperature are calculated analytically by using Laplace transform. The velocity and heat transfer of Prabhakar-like fractional natural convection flows of CNTs nanofluids are compared with those corresponding to classical thermal transport, which is described by Fourier's law. The effects of fractional and significant physical parameters are graphically interlined.