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Convective stability of ferromagnetic fluids can provide an adequate heat transfer via conventional convection due to a temperature gradient. This manuscript presents an analytical study for thermo-magnetized convection by means of non-integer order derivatives is investigated in which the core object is to show how to enhance, invert and suppress the convection modes based on local verses non-local kernels. Mathematical modeling is developed for the sake of magnetization depends upon governing equations of velocity, concentration and temperature profiles. Fractional treatments are invoked based on Fourier analysis and Laplace transforms to the dynamical equations govern the thermomagnetic convection. The analytical solutions of velocity, concentration and temperature have been established in terms of Mittage-Leffler E α − β t α and elementary functions. In order to have the performance of higher or lower susceptibility from thermomagnetic convection, profiles of velocity, concentration and temperature have been depicted separately by means of Atangana-Baleanu and Caputo-Fabrizio fractional operators for highlighting the immense impacts on ferromagnetic fluid flow. For the sake of novel outcomes of this study, it is observed that velocity is decreasing function of magnetic field when an increment in the amount of magnetic constant kicks off the augmentation of the Lorentz strength.

The convection, thermal conductivity, and heat transfer of hybrid nanofluid through nanoparticles has become integral part of several natural and industrial processes. In this manuscript, a new fractionalized model based on hybrid nanofluid is proposed and investigated by employing singular verses and non-singular kernels. The mathematical modeling of hybrid nanofluid is handled via modern fractional definitions of differentiations. The combined Laplace and Fourier Sine transforms have been configurated on the governing equations of hybrid nanofluid. The analytical expression of the governing temperature and velocity equations of hybrid nanofluid have been solved via special functions. For the sake of thermal performance, dimensional analysis of governing equations and suitable boundary conditions based on Mittage-Leffler function have been invoked for the first time in literature. The comparative analysis of heat transfer from hybrid nanofluid has been observed through Caputo-Fabrizio and Atangana-Baleanu differential operators. Finally, our results suggest that volume fraction has the decelerated and accelerated trends of temperature distribution and inclined and declined profile of heat transfer is observed copper and alumina nanoparticles.

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