Relative Magnetic Field and slipping effect on Casson dusty fluid of two phase fluctuating flow over inclined parallel plate

•The Casson fluid contains dust particles that are equally distributed and electrically conductive. the MFFRP or MFFRF.•The mathematical modeling was established as the set of partial differential equations for dusty brinkman fluid.•The perturb solution is to find out by incorporating Poincare–Lighthill perturbation technique.•It is possible to regulate the rate of heat transmission in a fluid by increasing the radiation parameter.•As η,N,K1,Gr and α are raised, the velocity of the fluid and the dust particles rise, but as β and M are raised, both velocities fall.