Legendre neural network-based computational study through hybrid particle swarm optimization for fractional unsteady flow of Sutterby fluid.

This study investigates the two-dimensional unsteady flow of a Sutterby fluid over a stretching surface under no slip boundary condition with additional effects. The governing fractional model develop with non-local behavior of fluid properties are handled via machine learning approach based on Legendre artificial neural network (LANN). The proposed LANN computational scheme is employ, supported by optimization techniques including particle swarm optimization PSO, fractional order particle swarm optimization FPSO, and a hybrid PSO-FPSO. A novel approach is used to solve the fractional-order momentum equation of Sutterby fluid, accurately capturing memory effects and the physics of complex boundary conditions, including wall velocity, wall squeezing, and porous medium effects, which are not addressed in prior studies. An increase in the fractional-order parameter are found to accelerate the flow, reflecting enhance the memory effects. The permeability parameter produced an opposing effect, reducing velocity due to the resistance of the porous medium. Similarly, the squeezing parameter exhibited a dual role, negative squeezing enhanced velocity, while positive squeezing suppressed fluid motion. furthermore, the higher values of magnetic number is represent to velocity profile upward. Converging exhibits that standard particle swarm optimization converges less quickly, while fractional particle swarm optimization and the hybrid approach accelerate, optimized and stability achieved. The limiting behaviour of the fitness function scrutinize that PSO, FPSO, and the combinations of PSO-FPSO tend to Residual mean squared of [Formula: see text], [Formula: see text], and [Formula: see text], respectively. These observance shows the deeply connection between non-integer formulating and better flow control values in determining fluid behavior. Generally, the non-integer order LANN method yields stability and rigorous solutions for intricate non-Newtonian fluid. The results is not only enriching the procedural knowledge of fractional order Sutterby model and also along with real life applications for food processing, bioengineering, polymer processing, and lubrication systems.