Analysis of food chain mathematical model under fractal fractional Caputo derivative.

In this article, the dynamical behavior of a complex food chain model under a fractal fractional Caputo (FFC) derivative is investigated. The dynamical population of the proposed model is categorized as prey populations, intermediate predators, and top predators. The top predators are subdivided into mature predators and immature predators. Using fixed point theory, we calculate the existence, uniqueness, and stability of the solution. We examined the possibility of obtaining new dynamical results with fractal-fractional derivatives in the Caputo sense and present the results for several non-integer orders. The fractional Adams-Bashforth iterative technique is used for an approximate solution of the proposed model. It is observed that the effects of the applied scheme are more valuable and can be implemented to study the dynamical behavior of many nonlinear mathematical models with a variety of fractional orders and fractal dimensions.

Numerical simulation on energy transfer enhancement of a Williamson ferrofluid subjected to thermal radiation and a magnetic field using hybrid ultrafine particles.

In this numerical investigation, completely developed laminar convective heat transfer characteristics of a Williamson hybrid ferronanofluid over a cylindrical surface are reported. This new model in 2D is engaged to examine the effects of the magnetic field, thermal radiation factor, volume fraction of ultrafine particles, and Weissenberg number with the help of the Keller box method. The numerical calculations are implemented at a magnetic parameter range of 0.4 to 0.8, volume fraction range of 0.0 to 0.1, and a Weissenberg number range of 0.1 to 0.8. The numerical outcomes concluded that the velocity increases when the thermal radiation parameter and the volume fraction of a nanoparticle are increased, but inverse impacts are obtained for the magnetic parameter and the Weissenberg number. The rate of energy transport increases with increasing thermal radiation and volume fraction, while it declines with increasing the magnetic parameter and Weissenberg number. The drag force shows a positive relationship with the thermal radiation parameter and has an opposite relationship with the Weissenberg number and the magnetic parameter. Furthermore, even when the magnetic field, thermal radiation, volume fraction, and Weissenberg number are all present, the heat transfer rate of Williamson hybrid ferronanofluid is greater than that of mono Williamson ferronanofluid.