Prabhakar-fractional simulations for the exact solution of Casson-type fluid with experiencing the effects of magneto-hydrodynamics and sinusoidal thermal conditions

This analysis inspects an unsteady and incompressible Casson-type fluid moving on a poured inclined oscillating plane with a ramped thermal profile. The physical effects of flow parameters cannot be investigated and studied using a memory effect, just like with regular PDEs. In this study, we have confabulated the solution of magnetised Casson-type fluid with the help of the best and most modified fractional definition, known as the Prabhakar-like thermal fractional derivative. An integral transforms scheme, namely Laplace transformation (LT) solves the dimensionless governed equations. The physical impacts of significant and fractional constraints are examined graphically and mathematically. As a result, we have confabulated that both thermal and momentum dynamics of flowing Casson fluid slow down with the increment in fractional constraint. Additionally, because of the thickness of the boundary layer, the Casson fluid parameter emphasises the dual character of flowing fluid dynamics.