Fractional Modeling of Non-Newtonian Casson Fluid between Two Parallel Plates

In this manuscript, fractional modeling of non-Newtonian Casson fluid squeezed between two parallel plates is performed under the influence magneto-hydro-dynamic and Darcian effects. The model fractionally transformed through mixed similarity transformations. As a result, partial differential equations (PDEs) are to ordinary equation (FODE). current modeling, continuity satisfied while momentum integral order recovered when parameter taken as ? = 1 . A modified homotopy perturbation algorithm used for solution analysis highly nonlinear fully equations. Obtained solutions errors compared with existing results from literature. Graphical also at normal radial velocity components different parameters. Analysis reveals that few parameters showing behavior in environment integer-order cases These findings affirm importance calculus terms more generalized physical phenomena.