On stretched magnetic surfaces, we present a numerical study of Casson nanofluids moving through porous materials. The Casson liquid model explains how non-Newtonian liquids behave. Numerical techniques are utilized to solve the nonlinear partial differential equations produced by similarity transformations. Results are gathered for the Nusselt number, skin friction coefficient, temperature and velocity. The impacts of physical variables on the flow and heat transfer characteristics of nanofluids are depicted in graphs. They include the Prandtl number, magnetic parameter, radiation parameter, porosity parameter and Casson parameter. Findings indicate that as the Casson nanofluid parameters are increased, the temperature profile rises but the velocity field decreases. With increasing magnetic parameters alone, it is possible to see a decrease in the thickness of the pulse boundary layer and an increase in the thickness of the thermal boundary layer. All the results are depicted in graphical representations.

In this research paper, we utilize an analytical technique to investigate the behavior of the Drinfeld-Sokolov-Wilson equation of arbitrary order. The implemented technique is an adequate composition of the Kharrat-Toma transform and the q-homotopy analysis approach. Here, a regularized form of the Hilfer-Prabhakar derivative of arbitrary order is used to formulate the problem. The Drinfeld-Sokolov-Wilson equation of arbitrary order is utilized to model the dispersive water waves and plays a very significant role in fluid dynamics. The results of the discussed model are presented graphically to show the efficiency and reliability of the obtained results.