Abstract:
In this manuscript, a new approach to study the fractionalized Oldroyd-B fluid flow based
on the fundamental symmetry is described by critically examining the Prabhakar fractional derivative
near an infinitely vertical plate, wall slip condition on temperature along with Newtonian heating
effects and constant concentration. The phenomenon has been described in forms of partial differential equations along with heat and mass transportation effect taken into account. The Prabhakar
fractional operator which was recently introduced is used in this work together with generalized
Fick’s and Fourier’s law. The fractional model is transfromed into a non-dimentional form by using
some suitable quantities and the symmetry of fluid flow is analyzed. The non-dimensional developed
fractional model for momentum, thermal and diffusion equations based on Prabhakar fractional
operator has been solved analytically via Laplace transformation method and calculated solutions
expressed in terms of Mittag-Leffler special functions. Graphical demonstrations are made to characterize the physical behavior of different parameters and significance of such system parameters
over the momentum, concentration and energy profiles. Moreover, to validate our current results,
some limiting models such as fractional and classical fluid models for Maxwell and Newtonian are
recovered, in the presence of with/without slip boundary wall conditions. Further, it is observed
from the graphs the velocity curves for classical fluid models are relatively higher than fractional fluid
models. A comparative analysis between fractional and classical models depicts that the Prabhakar
fractional model explains the memory effects more adequately.