A Novel PINN–ANFIS Framework for Fractional MHD Flow of Casson HCNTs for High Performance Thermal Systems

This study investigates a neural computing framework to analyze the unsteady MHD Darcy–Forchheimer flow (DFF) of water‐based Casson hybrid carbon nanotubes (HCNTs) over a stretching surface incorporating various slip effects and conformable fractional derivatives. The Casson HCNTs are widely used to optimize the efficiency of sophisticated heat transfer and energy systems due to their excellent thermal conductivity behavior and structural integrity. The governing flow models are converted into a system of nonlinear ordinary differential equations by employing proper transformation variables. These modified equations are numerically solved using physics‐informed neural networks (PINNs) and the bvp4c numerical solver. In addition, adaptive neuro‐fuzzy inference system (ANFIS) is used as hybrid computational framework that integrates artificial neural network (ANN) and fuzzy logic to forecast the solution profiles based on the numerical outcomes produced by the bvp4c solver. The PINN and ANFIS results exhibit excellent agreement with the bvp4c results, demonstrating the high prediction accuracy and reliability of the proposed models. The research findings demonstrated that the growing magnetic field and unsteady parameters weaken the fluid velocity field, whereas augmenting the nanoparticle volume fraction (NPVF) and thermal radiation parameters promote the temperature field. The nanofluid (NF) concentration field lowers with increasing value of chemical reaction parameter. The heat transmission gradient lowers for larger quantities of the thermal slip parameter. The outcomes of our research offer a useful framework for augmenting the functionality and efficiency of the high‐performance thermal systems in industrial and engineering domains.