Three different fractional models of Oldroyd-B fluid are considered in this work. Blood is taken as a special example of Oldroyd-B fluid (base fluid) with the suspension of gold nanoparticles, making the solution a biomagnetic non-Newtonian nanofluid. Based on three different definitions of fractional operators, three different models of the resulting nanofluid are developed. These three operators are based on the definitions of Caputo (C), Caputo–Fabrizio (CF), and Atnagana–Baleanu in the Caputo sense (ABC). Nanofluid is taken over an upright plate with ramped wall heating and time-dependent fluid velocity at the sidewall. The effects of magnetohydrodynamic (MHD) and porous medium are also considered. Triple fractional analysis is performed to solve the resulting three models, based on three different fractional operators. The Laplace transform is applied to each problem separately, and Zakian’s numerical algorithm is used for the Laplace inversion. The solutions are presented in various graphs with physical arguments. Results are computed and shown in various plots. The empirical results indicate that, for ramped temperature, the temperature field is highest for the ABC derivative, followed by the CF and Caputo fractional derivatives. In contrast, for isothermal temperature, the temperature field of C-derivative is higher than the CF and ABC derivatives, respectively. It was noticed that the velocity field for the ABC derivative is higher than the CF and Caputo fractional derivatives for ramped velocity. However, the velocity field for the Caputo fractional derivative is lower than the ABC and CF for isothermal velocity.

The industrial and engineering consumption of nanofluids is increased day by day due to successful implementation. The improved thermophysical properties play a vital role in the efficiency of nanofluids in convections processes. But this technology is not stopped here and reached to the next level by introducing hybrid nanofluids. Hence, this article is dedicated to focus on the mixed convection flow hybrid nanofluid. The hybridized nanoparticles of copper and alumina are dissolved in water as a base fluid to form a suspension. The Atangana-Baleanu fractional model is considered for flow demonstration over a vertical plate. The fractional PDE’s of the model is subjected to physical initial and boundary conditions. It is assumed that the electrically conducting laminar incompressible flow is under the influence of a magnetic field of variable direction. The Laplace transform technique is implemented to develop exact solutions for the problem under consideration. To explore the behavior of flow parameters, the obtained solutions are numerically computed and displayed in various figures with a physical explanation. It is found that the velocity and temperature profiles behave alike for fractional parameter α . Both the profiles decrease with increasing values of α . However, the trend of these profiles is opposite for volume concentration Φhnf of hybrid nanofluid. The velocity profile decreases with increasing values of Φhnf whereas, the temperature profile increases with increasing values of Φhnf .

Introduction of fractional derivatives to the mechanics of fluid flow is relatively new. Even though the exact geometrical representations of fractional derivatives on fluid mechanics have not been discovered, recent literatures have proven that it is a paradox that will be useful in the future. Meanwhile, Riga plates are actuators that is convenient for controlling the velocity of fluid flows. Widely used in the field of marine engineering, the properties of fluid flowing over Riga plates are worth investigating. Thus, the aim of this study is to investigate the analytical solutions of an unsteady incompressible Casson nanofluid flowing over a Riga plate with presence of Newtonian heating. Carboxymethyl Cellulose (CMC) water was used as a prime example of Casson fluid with Copper-Oxide (CuO) nanoparticles. Coupled with a non-Newtonian fluid, the Casson fluid, and the Caputo-Fabrizio fractional derivative, the analytical solutions obtained will be beneficial in the engineering world as a tool for validating experimental and numerical studies. Through this study, analytical solutions were obtained and the profiles of both velocity and temperature of fluid with variations in parameters were investigated. It is observed that variations in the fractional derivative parameter produces a spectrum of solutions that abides the initial and boundary conditions set. An amplification of the modified Hartmann number increases both the velocity and temperature profiles, while an amplification of the nanoparticle volume fraction decreases the velocity profile but increase the temperature profile.