This paper presents a modelling of nanofluid flow using Caputo fractional derivatives through conservative equations of mass and momentum, and provides an exact solution on un-steady convective flow over a vertical plate with the mass diffusion effect, in association with an energy equation. H2O is the base liquid with clay nanoparticles floating in it in a uniform way. Boussinessq’s approach is used in the momentum equation for pressure gradient. The non-dimensional fluid temperature, species concentration and fluid transport are derived together with Jacob Fourier sine and Laplace transform techniques in terms of exponential decay function, and the inverse is computed further in terms of the Mittag-Leffler function. The impact of various physical quantities is interpreted with the fractional order of the Caputo derivatives. The obtained temperature, transport and species concentration profiles show behaviors for 0 < α < 1, where α is the fractional parameter. The rate of heat and mass transfer coefficients for the significance of physical quantities of interest are also obtained and presented through graphs. The impact of the nanoparticle volume fraction on the flow field is observed. At larger values of the fractional parameter, the velocity, temperature, and concentration distributions grow more quickly. In addition to that, it is found the concentration profiles behave in the opposite way for the volume fraction of nanofluids.