Unsteady two dimensional flow of non-newtönian fractional Casson fluid for an edge with heated boundaries

This study explores the transient flow and thermal behavior of incompressible non-Newtonian fluids, with a particular emphasis on Casson and fractional Casson models, which are widely applied in blood flow, lubricants, and polymer processing. The Casson model, characterized by shear-thinning and yield stress effects, is extended using fractional derivatives to capture memory-dependent dynamics and complex non-Newtonian responses. Advanced mathematical techniques, including Fourier and Fourier sine transforms, are employed to derive exact analytical solutions of the governing equations under oscillatory boundary conditions, while accounting for the influence of magnetic fields, porous media, and heat transfer. Mathematica is used to obtain solutions and generate graphical representations. Instead of listing individual parameter effects, the study highlights the collective role of fractional-order terms, oscillatory forcing, magnetic interactions, and thermal gradients in shaping both velocity and temperature fields. The results provide general insights into how fractional dynamics and transport properties influence system stability, oscillatory behavior, and flow persistence. In conclusion, the work establishes a unified framework for analyzing fractional Casson fluid flows and demonstrates the value of fractional calculus in modeling memory effects in non-Newtonian systems. The findings are expected to support industrial and biomedical applications and suggest future directions including three-dimensional extensions, relaxation of periodic boundary conditions, and direct engineering applications.