This study explores transient magnetohydrodynamic (MHD) heat and mass transfer in the flow of a hybrid nanofluid over a stretching surface, considering both steady and unsteady scenarios. The investigation incorporates chemical reactions, slip boundary conditions, and the effects of thermal radiation. The hybrid nanofluid, composed of copper oxide (CuO) and gold (Au) nanoparticles in a water-based fluid, demonstrates enhanced thermal performance compared with base fluids. Key findings reveal that higher nanoparticle concentrations significantly improve heat transfer, highlighting the potential of hybrid nanofluids in advanced thermal management applications. Additionally, machine learning models effectively predict heat transfer characteristics with high accuracy (R² = 0.99), showcasing their effectiveness in complementing traditional numerical methods. These findings contribute to the understanding of hybrid nanofluids in complex thermal systems and highlight the utility of emerging computational tools for thermal analysis.

This paper is devoted to studying the existence and uniqueness of solutions of fuzzy nabla dynamic equations on time scales under Hukuhara differentiability. We apply the Banach contraction mapping principle to establish existence and uniqueness solution for fuzzy nabla initial value problems on time scales and also obtain existence result using Ascoli’s theorem and Schauder’s fixed point theorem.

This paper mainly deals with introducing and studying the properties of generalized nabla differentiability for fuzzy functions on time scales via Hukuhara difference. Further, we obtain embedding results on ${\mathbb{E}}_n$ for generalized nabla differentiable fuzzy functions. Finally, we prove a fundamental theorem of a nabla integral calculus for fuzzy functions on time scales under generalized nabla differentiability. The obtained results are illustrated with suitable examples.