This work presents an analytical study of unsteady, one-dimensional magnetohydrodynamic flow of a Casson–Brinkman fluid over an infinite vertical plate, incorporating heat and mass transfer, internal heat generation, and a first-order chemical reaction. The plate velocity, temperature, and concentration are time-dependent, with ramped boundary conditions, and the governing equations account for a transverse magnetic field. Using Buckingham’s π-theorem, the model is nondimensionalized, introducing key parameters including the Grashof numbers, Hartmann number, Prandtl number, Schmidt number, Casson parameter, and Brinkman parameter. The classical Fourier and Fick laws are extended using the Caputo fractional derivative to capture memory effects, yielding a time-fractional model. The coupled fractional partial differential equations are solved analytically via Laplace transforms, and the effects of the fractional order and the physical parameters on the velocity, temperature, and concentration profiles are graphically analyzed. Results reveal that the fractional parameter significantly varies the heat and mass transfer profiles.

To investigate the effects of fractional order (), nanoparticle volume fraction (), magnetic field strength (), and Brinkman permeability () on both flow and heat transfer characteristics, a detailed parametric and statistical analysis is conducted. The statistical regression analysis shows that the volume fraction of nanoparticles and temperature have a strong positive correlation (coefficient = 0.94, p = 0.021) indicating that Mo2C MXene is an excellent heat absorption. On the other hand, the fractional parameter α has a strong negative effect on temperature field (coefficient = − 0.086, p < 0.001), which emphasizes its importance in describing the effects of thermal memory. The findings also indicate that, although MXene nanoparticles significantly increase thermal transport, an augmentation in magnetic field strength and Brinkman resistance cause a resistive Lorentz force and frictional drag, respectively, to prevent fluid flow. These results are physically informative about non-Fourier heat transfer in MXene-based nanofluids as well as offer invaluable information to developing high-performance thermal management systems and solar-energy applications.