Modeling and prediction of fractional-order MHD hybrid nanofluid flow using CPCF derivatives and LMS-based neural networks

This study investigates the unsteady natural convection flows of an inclined magnetohydrodynamic (MHD) Casson hybrid nanofluid over an unbounded vertical plate with fractional thermal transport. To model thermal flux, the modern Constant Proportional Caputo-Fabrizio (CPCF) Derivative is employed. This modification enhances the accuracy of fractional-order thermal transport modeling and captures the non-singular finite-memory thermal relaxation that the standard Caputo-Fabrizio kernel cannot represent consistently. After formulating the physical problem, the governing equations are converted into their non-dimensional format and analyzed using the Laplace transform (LT) technique. To obtain the semi-analytical solutions, numerical inverse methods such as the Gaver-Stehfest algorithm and Tazou's approach are utilized. The effects of fractional-order parameters and flow characteristics on momentum and temperature fields are analyzed graphically using MATHCAD 15 software. Furthermore, a machine learning approach is implemented on temperature to enhance predictive accuracy. The Levenberg-Marquardt scheme within a Neural Network Algorithm (LMS-NNA) is utilized to approximate the governing flow equations efficiently. This integration of machine learning with fractional-order modeling provides deeper insights into the complex dynamics of the system. Ultimately, the CPCF kernel provides a more realistic finite-memory response and better numerical conditioning, giving practical improvement in fractional-order heat-transport prediction. The direct applicability of this work to industrial and biomedical technologies lies in providing a highly accurate and tunable predictive model for complex fluid systems.