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Nanofluids are used to achieve maximum thermal performance with the smallest concentration of nanoparticles and stable suspension in conventional fluids. The effectiveness of nanofluids in convection processes is significantly influenced by their increased thermophysical characteristics. Based on the characteristics of nanofluids, this study examines generalized Brinkman-type nanofluid flow in a vertical channel. Three different types of ultrafine solid nanoparticles such as GO, Al2O3Al2O3, and TiO2TiO2 are dispersed uniformly in regular water to form nanofluid.  Partial differential equations (PDEs) are used to model the phenomena. Fick’s and Fourier’s laws of fractional order were then used to formulate the generalized mathematical model. The exact solution of the generalized mathematical model has been obtained by the joint use of Fourier sine and the Laplace transform (LT) techniques. The obtained solution is represented in Mittag-Leffler function. To analyze the behavior of fluid flow, heat and mass distribution in fluid, the obtained solution was computed numerically and then plotted in response to different physical parameters. It is worth noting from the analysis that the heat transfer efficiency of regular water has been improved by 25% by using GO nanoparticles, 23.98% by using Al2O3Al2O3, and 20.88% by using TiO2TiO2.