Fractional analysis for multiple solutions of thermodynamic model of Casson fluid under hydrodynamic and non-hydrodynamic optimization

This study investigates the flow behavior of a non-Newtonian Casson fluid influenced by hydromagnetic and non-hydromagnetic effects over an oscillating plate, subject to combined gradients of temperature and mass concentration. The analysis is framed within the context of linear fractional differential equations incorporating the Caputo-Fabrizio fractional derivative with a non-singular kernel. A mathematical model is developed, employing a linear boundary condition to characterize the temperature distribution, mass concentration, and velocity profiles. The governing equations are first non-dimensionalized and then extended into their fractional forms. An analytical solution is obtained using integral transform techniques, specifically the Laplace transform with its inversion and the Fourier sine transform with inversion. The break down the data analysis process under rheological variation for temperature and concentration is explored through which generalization and comparison is investigated. The key findings are focused on the flow and heat transfer characteristics, examining the influence of key dimensionless parameters. Moreover, the comparison between fractional and classical approaches are found in excellent agreement.