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• This work investigates the radiative MHD fluid flow through a porous vertical plate. • The effects of mass and heat transfer through ramped temperature is considered. • The thermal radiation, mixed convection and slip conditions are used. • The Atangana-Baleanu (AB) time-fractional derivative is used for numerical results. • The Laplace scheme, Stehfest and Tzou's algorithms are used to find semi-analytical solution. In this study, we have investigated the magnetohydrodynamics(MHD) fluid flow through a porous medium flowing on anerect vertical plate. The effects of mass and heat transfer through ramped temperature, thermal radiation, and slip conditions in the energy equation are also considered. To enhance the innovation of this article, the recent definition of fractional derivative operator i.e. Atangana-Baleanu (AB) time-fractional derivative, is used to explore the numerical results of the problem.The semi-analytical solution of fractional dimensionless leading equations is obtained by using the Laplace scheme and some numerical methods namely Stehfest and Tzou's algorithms. Some specialcases of velocity distribution are discussed whose physical applications are well-defined in the literature. The obtained results are illustrated graphically and numerically by changing the values ofdifferent parameters. A decayinh change in heat transfer and velocity profile is noticed for fractional parameter β. [ABSTRACT FROM AUTHOR]