In this article, the free convection flow of second-grade nanofluids based on carbon nanotubes (CNTs) with Prabhakar-like fractional and Newtonian heating over a vertical plate has been studied. The fractional model of governing equations is defined by the time-dependent fractional Prabhakar derivative. Using the Laplace transform method, analytical solutions are determined for the dimensionless thermal and velocity profiles. Prabhakar-like fractional second-grade fluids with generalized thermal transport velocity and heat transfer are compared with ordinary second-grade fluids with ordinary thermal transport and ordinary viscous fluids with classical Fourier thermal flux. The effects of fractional and physical parameters are expressed graphically.