MHD Radiative Casson Fluid Flow with Ramped Influence through a Porous Media via Constant Proportional Caputo Approach

The current study focuses on investigating the solutions of the mathematical model in the form of special functions. The phenomenon is described by a set of partial differential equations, which are then transformed into non-dimensional form. In order to improve the rheology of the Casson fluid, a fractional model is developed by using a new fractional operator Constant Proportional Caputo (CPC) approach to investigate and formulate the dynamics of Casson fluid flow and heat transfer phenomena subjected to ramped wall temperature. The fluid flow is elaborated near an infinitely vertical plate with characteristics velocity \(u_0\) $u_0$ . We began by introducing appropriate variables to transform the mathematical model into non-dimensional form. Laplace transformation operator applied to gain the solution from fractional model, then obtained results expressed in the form of well-known special functions. The influence of various pertinent parameters involving in the solution was carefully examined to unveil intriguing findings. Upon comparison, we observed that the CPC approach yielded better results, after comparison with classical models documented in the literature, with graphical representations provided to illustrate these outcomes. To comprehensively analyze the dynamics of the proposed problem, physical influence of various parameters is studied and repercussions are graphically highlighted and discussed. Additionally, we derived results in a limiting sense, including Casson and viscous fluid models transitioning from the classical form to the fractionalized fluid model.