This research explores the impact of the relative magnetic effect on the Couette flow of dusty Casson fluid between two parallel Riga plates. The mathematical model is based on a set of partial differential equations that describe the behavior of the dusty Casson fluid in interaction with the Riga plate. To convert this system of equations to its dimensionless form, appropriate transformations are used, and to solve this system numerically, explicit finite difference methods are applied to it. A graphical representation has been presented by using MatLab software for a comprehensive understanding of the effect of various non-dimensional parameters such as pressure gradient parameter (α), Casson parameter (β), modified Hartmann number (H_a), fluid concentration parameter (R), particle mass parameter (G), Eckert number (E_c), Prandtl number (P_r), and temperature relaxation time parameter (L₀) on the velocity distributions u (or u_p) and on the temperature distributions θ (or θ_p), including shear stress and Nusselt number for both clean and dust fluid particles. The impacts of these parameters on the above-mentioned distributions have been discussed with their physical significance, taking the variation of any one of those parameters and with fixed values of α =1, β = 2, H_a=1, R = 0.5, G = 0.5, E_c = 0.01, P_r = 0.71, and L₀ =0.8. The results reveal significant effects of relative magnetic fields on both clean fluid and dust particle motion.

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