Abstract
The Prabhakar fractional derivative model is not studied in the open literature for the Casson fluid model when the vertical plate exhibits linear and quadratic translations with constant heating. Therefore, this study deals with the thermal transport of sodium alginate (C6H9NaO7) over a vertical plate with a constant temperature. Since the classical PDEs are incapable of analyzing and investigating the physical impact of flow variables with memory effects, a fractional derivative model is developed using the Prabhakar fractional derivative approach. Two different types of plate translations (linear and quadratic) are considered. The non-dimensional governing equations are transformed into a fractional model and solved using the Laplace transformation (L.T) technique. The effects and behavior of significant physical parameters and fractional order parameters are studied graphically and discussed. As a consequence, it is found that as fractional limitations are increased, the thermal and momentum profiles drop. In addition, the momentum profile in the case of quadratic translation (variable acceleration) shows a higher magnitude than the case of linear translation (constantly accelerated plate).