Fractional magnetohydrodynamic Casson fluid flow with thermal radiation and buoyancy effects: a constant proportional Caputo model

This research examines the magnetohydrodynamic (MHD) flow of a Casson flow over an oscillating vertically plate, incorporating thermal radiation and buoyancy effects using the constant proportional Caputo (CPC) fractional derivative. By introducing memory and nonlocal effects, the fractional derivative provides an enhanced framework for accurately capturing the coupled behavior of fluid dynamics, mass, and heat transfer. Applying the Laplace transform, the fractional partial differential equations that control the flow are transformed into ordinary differential equations, which are then solved numerically by Stehfest’s and Tzou’s techniques. This methodology enables detailed analysis of key physical parameters, such as magnetic fields, thermal radiation, and buoyant forces, on the velocity, temperature, and concentration distributions. Results reveal that the fractional parameter significantly refines the concentration, temperature, and velocity profiles, offering novel insights into the dynamics of MHD flows under thermal and concentration gradients. The model is validated against prior work, showing excellent agreement in limiting cases and confirming the robustness of the approach. The study’s findings are applicable to high temperature plasmas, nuclear reactor cooling systems, and power generation technologies, contributing an advanced analytical framework for exploring complex fluid dynamics in interdisciplinary engineering and physical contexts.