Thermal and concentration diffusion impacts on MHD Maxwell fluid: A generalized Fourier's and Fick's perspective

In this article, a new approach to study the fractionalized Maxwell fluid is described by the Prabhakar fractional derivative near an exponentially accelerated vertical plate together with exponentially variable velocity, energy and mass diffusion through a porous media is critically examined. The phenomena 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 fractionalized model is transfromed into non-dimensional form by using some suitable dimensionless quantities. 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 demonstration are made to characterized the physical behavior of different parameters and significance of such system parameters over the momentum, concentration and energy profiles. Moreover, for results validation, comparative study among limiting models derived from fractionalized Prabhakar Maxwell fluid such as fractional and classical fluid models for Maxwell and Newtonian are performed. Further, it is observed from the graphs the valocity curves for classical fluid models relatively higher as compared to fractional fluid models, and fractional approach is more realistic and convenient as compared to classical approach.