Dual thermal analysis of magnetohydrodynamic flow of nanofluids via modern approaches of Caputo–Fabrizio and Atangana–Baleanu fractional derivatives embedded in porous medium

This manuscript investigates the temperature difference versus temperature or time and the effects of newly introduced fractional operators, namely Caputo–Fabrizio and Atangana–Baleanu fractional derivatives, on the magnetohydrodynamic flow of nanofluid in a porous medium. Three different types of nanoparticles are suspended in ethylene glycol, namely titanium oxide, copper and aluminum oxide. The mathematical modeling of the governing equations is developed by the modern fractional derivatives. The general solutions for velocity field and temperature distribution have been established by invoking Laplace transforms, and obtained solutions are expressed in terms of special functions, namely Fox-H function $${\mathbf{H}}_{\upalpha ,\upbeta + 1}^{1,\alpha } \left( F \right)$$Hα,β+11,αF and $${\mathbf{M}}_{\upbeta ,\upgamma }^{\alpha } \left( F \right)$$Mβ,γαF Mittag-Leffler functions. Dual solutions have been analyzed by graphical illustrations for the influence of pertinent parameters on the motion of a fluid. The base fluid and three different types of nanoparticles have intersecting similarities and differences in the heat transfer and fluid flows. The results show the reciprocal behavior of different types of nanoparticles which are suspended in ethylene glycol via Caputo–Fabrizio and Atangana–Baleanu fractional operators.