Machine learning approach of Casson hybrid nanofluid flow over a heated stretching surface

The present investigation focused on the influence of magnetohydrodynamic Gold-Fe3O4 hybrid nanofluid flow over a stretching surface in the presence of a porous medium and linear thermal radiation. This article demonstrates a novel method for implementing an intelligent computational solution by using a multilayer perception (MLP) feed-forward back-propagation artificial neural network (ANN) controlled by the Levenberg-Marquard algorithm. We trained, tested, and validated the ANN model using the obtained data. In this model, we used blood as the base fluid along with Gold-Fe3O4 nanoparticles. By using the suitable self-similarity variables, the partial differential equations (PDEs) are transformed into ordinary differential equations (ODEs). After that, the dimensionless equations were solved by using the MATLAB solver in the Fehlberg method, such as those involving velocity, energy, skin friction coefficient, heat transfer rates and other variables. The goals of the ANN model included data selection, network construction, network training, and performance assessment using the mean square error indicator. The influence of key factors on fluid transport properties is presented via tables and graphs. The velocity profile decreased for higher values of the magnetic field parameter and we noticed an increasing tendency in the temperature profile. This type of theoretical investigation is a necessary aspect of the biomedical field and many engineering sectors

Flows with Slip of Oldroyd-B Fluids over a Moving Plate

A general investigation has been made and analytic solutions are provided corresponding to the flows of an Oldroyd-B fluid, under the consideration of slip condition at the boundary. The fluid motion is generated by the flat plate which has a translational motion in its plane with a time-dependent velocity. The adequate integral transform approach is employed to find analytic solutions for the velocity field. Solutions for the flows corresponding to Maxwell fluid, second-grade fluid, and Newtonian fluid are also determined in both cases, namely, flows with slip on the boundary and flows with no slip on the boundary, respectively. Some of our results were compared with other results from the literature. The effects of several emerging dimensionless and pertinent parameters on the fluid velocity have been studied theoretically as well as graphically in the paper

Numerical simulation of fractional-order two-dimensional Helmholtz equations

In this paper, we investigate the exact solutions of several fractional-order Helmholtz equations using the homotopy perturbation transform method. We specify sufficient requirements for its convergence and provide error estimations. The homotopy perturbation transform method yields a quickly converging succession of solutions. Solutions for various fractional space derivatives are compared to present approaches and explained using figures. Appropriate parameter selection produces approximations identical to the exact answer. Test examples are provided to demonstrate the proposed approach's precision and competence. The results demonstrate that our system is appealing, user-friendly, dependable, and highly effective

Dynamic complexity of a slow-fast predator-prey model with herd behavior

The complex dynamics of a slow-fast predator-prey interaction with herd behavior are examined in this work. We investigate the presence and stability of fixed points. By employing the bifurcation theory, it is shown that the model undergoes both a period-doubling and a Neimark-Sacker bifurcation at the interior fixed point. Under the influence of period-doubling and Neimark-Sacker bifurcations, chaos is controlled using the hybrid control approach. Moreover, numerical simulations are carried out to highlight the model's complexity and show how well they agree with analytical findings. Employing the slow-fast factor as the bifurcation parameter shows that the model goes through a Neimark-Sacker bifurcation for greater values of the slow-fast factor at the interior fixed point. This makes sense because if the slow-fast factor is large, the growth rates of the predator and its prey will be about identical, automatically causing the interior fixed point to become unstable owing to the predator's slow growth

Magnetohydrodynamic Free Convection Flows with Thermal Memory over a Moving Vertical Plate in Porous Medium

The unsteady hydro-magnetic free convection flow with heat transfer of a linearly viscous, incompressible, electrically conducting fluid near a moving vertical plate with the constant heat is investigated. The flow domain is the porous half-space and a magnetic field of a variable direction is applied. The Caputo time-fractional derivative is employed in order to introduce a thermal flux constitutive equation with a weakly memory. The exact solutions for the fractional governing differential equations for fluid temperature, Nusselt number, velocity field, and skin friction are obtained by using the Laplace transform method. The numerical calculations are carried out and the results are presented in graphical illustrations. The influence of the memory parameter (the fractional order of the time-derivative) on the temperature and velocity fields is analyzed and a comparison between the fluid with the thermal memory and the ordinary fluid is made. It was observed that due to evolution in the time of the Caputo power-law kernel, the memory effects are stronger for the small values of the time t.  Moreover, it is found that the fluid flow is accelerated / retarded by varying the inclination angle of the magnetic field direction

Transient Electro-osmotic Slip Flow of an Oldroyd-B Fluid with Time-fractional Caputo-Fabrizio Derivative

In this article, the electro-osmotic flow of Oldroyd-B fluid in a circular micro-channel with slip boundary condition is considered. The corresponding fractional system is represented by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Closed form solutions for the velocity field are acquired by means of Laplace and finite Hankel transforms. Additionally, Stehfest’s algorithm is used for inverse Laplace transform. The solutions for fractional Maxwell, ordinary Maxwell and ordinary Newtonian fluids are obtained as limiting cases of the obtained solution. Finally, the influence of fractional and some important physical parameters on the fluid flow are spotlighted graphically

Transient MHD Convective Flow of Fractional Nanofluid between Vertical Plates

Effects of the uniform transverse magnetic field on the transient free convective flows of a nanofluid with generalized thermal transport between two vertical parallel plates have been analyzed. The fluid temperature is described by a time-fractional differential equation with Caputo derivatives. Closed form of the temperature field is obtained by using the Laplace transform and fractional derivatives of the Wright’s functions. A semi-analytical solution for the velocity field is obtained by using the Laplace transform coupled with the numerical algorithms for the inverse Laplace transform elaborated by Stehfest and Tzou. Effects of the derivative fractional order and physical parameters on the nanofluid flow and heat transfer are graphically investigated

Weighted Ostrowski type inequalities via Montgomery identity involving double integrals on time scales

In this paper, the Montgomery identity is generalized for double integrals on time scales by employing a novel analytical approach to develop the generalized Ostrowski type integral inequalities involving double integrals. Some inimitable cases are discussed for different parameters and parametric functions. Moreover, applications to some particular time scales are also presented

A robust MADM-approach to recruitment-based pattern recognition by using similarity measures of interval-valued fuzzy hypersoft set

Interval-valued fuzzy hypersoft set ($\mathbb{IVFHSS}$) is considered a pertinent fuzzy set-like model that is the combination of an interval-valued fuzzy set and a hypersoft set. It is more flexible and trustworthy for dealing with information-based uncertainties due to the consideration of interval-based hypersoft settings. This kind of setting enables the decision makers to approximate the alternatives in terms of interval-type opinions by considering multiple arguments concurrently. These features make it a fitting model for dealing with uncertain decision-making scenarios like the recruitment process. The vagueness arises in the recruitment process when the data obtained is hesitant. The analogous educational norms among the candidates may increase its complexity. Evaluation techniques focus on leveling hypersoft sets for grading several alternatives based on multi-arguments. When several alternatives have an identical status, such grading systems frequently encounter problems, making it challenging for decision-makers to select the preeminent alternative. This settlement of such an issue is the basis of this article. Thus, in this study, first the axiomatic notions of similarity measures between $\mathbb{IVFHSS}s$ are characterized, and then their relevant theorem is proved. In order to provide a consistent decision-support framework for the recruitment process, a robust algorithm is proposed. Finally, the effectiveness, feasibility, and efficiency of the proposed model are demonstrated through the depiction of recruitment-based pattern recognition

Impact of couple stress and variable viscosity on heat transfer and flow between two parallel plates in conducting field

This study explores the flow properties of a couple stress fluid with the consideration of variable viscosity and a uniform transverse magnetic field. Under the effect of irreversible heat transfer, a steady fluid flow has taken place between two parallel inclined plates. The fluid flows due to gravity and the constant pressure gradient force. The plates are fixed and isothermal. The governing equations have been solved analytically for velocity and temperature fields. The total rate of heat flow and volume flow across the channel, skin friction, and Nusselt number at both plates are calculated and represent the impacts of relevant parameters through tables and graphs. The findings show that velocity, temperature, and the total rate of heat flow across the channel are enhanced by increasing the couple stress parameter and the viscosity variation parameter, while increasing the values of the Hartmann number reduces them