Fractional-order modelling and analytical solutions for MHD casson fluid flow in an inclined channel with heat and mass transfer.

This study investigates the unsteady magnetohydrodynamic (MHD) flow of a Casson fluid in an inclined channel using a fractional calculus framework. The research aims to overcome limitations of classical formulations by incorporating Caputo time-fractional derivatives into generalized Fourier and Fick laws, enabling the capture of memory effects and non-local transport phenomena in viscoplastic fluids. Governing equations are fractionalized and solved exactly for velocity, temperature, and concentration profiles using a combined Laplace-Fourier sine transform technique, with solutions validated against physical boundary conditions. The results show that fractional-order modelling predicts higher heat transfer rates but lower mass transfer efficiency compared with the classical case, and effectively captures the transition of Casson fluids toward Newtonian behaviour. Stronger magnetic fields significantly suppress fluid motion due to enhanced Lorentz forces. These findings provide a validated analytical framework for the design and optimisation of laminar, non-reactive MHD Casson fluid systems in inclined biomedical channels, polymer ducts, and sloped heat exchangers, within the parameter ranges modelled, and advance the theoretical understanding of fractional MHD flows.