Fractal–Fractional Michaelis–Menten Enzymatic Reaction Model via Different Kernels

In this paper, three new models of fractal–fractional Michaelis–Menten enzymatic reaction (FFMMER) are studied. We present these models based on three different kernels, namely, power law, exponential decay, and Mittag-Leffler kernels. We construct three schema of successive approximations according to the theory of fractional calculus and with the help of Lagrange polynomials. The approximate solutions are compared with the resulting numerical solutions using the finite difference method (FDM). Because the approximate solutions in the classical case of the three models are very close to each other and almost matches, it is sufficient to compare one model, and the results were good. We investigate the effects of the fractal order and fractional order for all models. All calculations were performed using Mathematica software.

Influence of Thermal Radiation on MHD Fluid Flow over a Sphere

The current perusal investigation was carried out for the result of a chemical reaction and Schmidt number on magnetohydrodynamic fluid flow towards a Sphere with Rosseland approximation. The Roseland estimate is utilized to portray the radiative heat transition in the energy condition. The crucial equations of continuity, thermal and solutal boundary layers are reassembled into sets of nonlinear models. The highly nonlinear partial differential models are converted into a nonlinear ordinary differential structure through the proper dimensionless quantities. The numerical arrangements of standard differential structures have been procured by applying the fourth-order Runge-Kutta-Fehlberg strategy with shooting technique through MATHEMATICA software. The quantities of physical interest are graphically presented and discussed in detail. Correlation with past writing results is additionally done and is discovered to be excellent concurrence with those distributed before.

Study on the Kinetics of a Special Particle Swarm

For randomly-moving-particle swarm, the past researches only focused on its whole behavior and few people have studied the special particle swarm formed in it, which leading to the phenomenon and reasons for the spontaneous aggregation of particles in the special particle swarm being still unknown. For such a special particle swarm, we have previously studied the causes of its special relativity phenomenon. Here we show the causes of spontaneous aggregation of “randomly moving” particles. The diffusion kinetics of particles in a special circumstance (that is, in a moving reference frame $\mathcal{R}_u$ relative to the stationary reference frame $\mathcal{R}_0$) are studied theoretically. For the first time, the effects of the location aggregation and velocity direction aggregation of randomly moving particles on the diffusion coefficient are considered, and the corresponding generalized diffusion equation is deduced employing concise mathematical logic and Mathematica software.

Generalized exponential rational function for distinct types solutions to the conformable resonant Schrödinger’s equation

The generalized exponential rational function method, which is one of the strong methods for solving nonlinear evolution equations, is applied to the conformable resonant nonlinear Schrödinger’s equation in this study. This equation plays a significant role in nonlinear fiber optics. It also has many important applications in photonic crystal fibers. The procedure implemented in this paper can be recommended in solving other equations in the field. All calculations and graphing are performed using powerful symbolic computational packages in Mathematica software. All calculations and graphing are performed using powerful symbolic computational packages in Mathematica software.

New Optical Soliton Solutions to the Fractional Hyperbolic Nonlinear Schrödinger Equation

This paper is aimed at investigating the soliton solutions of the hyperbolic nonlinear Schrödinger equation. Exact analytical solutions of the model are acquired through applying an integration method, namely, the Sine-Gordon method. It is observed that the method is able to efficiently determine the exact solutions for this equation. Graphical simulations corresponding to some of the results obtained in the paper are also drawn. These results can help us better understand the behavior and performance of this model. The procedure implemented in this paper can be recommended in solving other equations in the field. All calculations and graphing are performed using powerful symbolic computational packages in Mathematica software.

Computational analysis of hydromagnetic boundary layer stagnation point flow of nano liquid by a stretched heated surface with convective conditions and radiation effect

In this study, the boundary layer phenomena for stagnation point flow of water-based nanofluids is being observed with the upshot of MHD and convective heating on a nonlinear stretching surface. To develop a fundamental flow model, a boundary layer approximation is done, which signifies time-dependent momentum, energy, and concentration expressions. Through a proper transformation framework, the modeled boundary layer partial differential equations (PDEs) have been diminished to a dimensionless system of nonlinear ordinary differential equations (ODEs). With the assistance of a built-in algorithm in Mathematica software, the fundamental flow equations are analyzed numerically by imposing a shooting technique explicitly. A stability and convergence analysis were also unveiled, and the ongoing investigation was found to have converged. The effect of mathematical abstractions on velocity, energy, and concentration is plotted and discussed. The influence of skin-friction and Nusselt number on the sheet are debated for the various values of important parameters.

An Efficient Non-Parametric Statistical Test for Assessing Some Treatment Methods of Clinical Data

The recent rapid spread of deadly epidemics have precipitated an urgent need to speed up the development of different treatments, as well as methods of evaluating their efficacy. The first step towards this is the collection of data relating to the cure rate in groups of patients who have had different treatments applied to them. As most of the available data in these cases is random, it is now the role of statisticians to provide efficient statistical tests to assess the treatment methods through the data. This research aims to provide a new statistical test with high efficiency to reach the right decision with accurate results as quickly as possible using parallel computing algorithms through Wolfram Mathematica software.

On the Statistical Discrepancy and Affinity of Priority Vector Heuristics in Pairwise-Comparison-Based Methods

There are numerous priority deriving methods (PDMs) for pairwise-comparison-based (PCB) problems. They are often examined within the Analytic Hierarchy Process (AHP), which applies the Principal Right Eigenvalue Method (PREV) in the process of prioritizing alternatives. It is known that when decision makers (DMs) are consistent with their preferences when making evaluations concerning various decision options, all available PDMs result in the same priority vector (PV). However, when the evaluations of DMs are inconsistent and their preferences concerning alternative solutions to a particular problem are not transitive (cardinally), the outcomes are often different. This research study examines selected PDMs in relation to their ranking credibility, which is assessed by relevant statistical measures. These measures determine the approximation quality of the selected PDMs. The examined estimates refer to the inconsistency of various Pairwise Comparison Matrices (PCMs)—i.e., W = (wij), wij > 0, where i, j = 1,…, n—which are obtained during the pairwise comparison simulation process examined with the application of Wolfram’s Mathematica Software. Thus, theoretical considerations are accompanied by Monte Carlo simulations that apply various scenarios for the PCM perturbation process and are designed for hypothetical three-level AHP frameworks. The examination results show the similarities and discrepancies among the examined PDMs from the perspective of their quality, which enriches the state of knowledge about the examined PCB prioritization methodology and provides further prospective opportunities.

Analytical Study of the Automatic Ventilation System for the Intake of Polluted Air from the Pigsty

The microclimate of a pigsty is determined by the combination of temperature, relative humidity, chemical and mechanical composition of the air, which have a significant impact on animal productivity and must be maintained within strict limits due to the physiological needs and capabilities of animals. An appropriate ventilation system has been created to ensure the removal of air from the pigsty. The purpose of the study is to establish the dependence of the operating parameters of the automatic ventilation system on the air quality in the pigsty, taking into account the permissible concentrations of gases. The developed automatic ventilation system for polluted air intake is located in the middle of the livestock house under the ceiling and consists of a central air duct, to which air intake pipes are connected. Air intake pipes are placed in the middle above each pen where animals are kept. Intake dampers with servomechanisms, temperature, humidity, and air quality sensors are installed at the inlet of the air intake pipes. The outlet of the central air intake duct is connected to the exhaust fan. Intake dampers with servomechanisms and sensors of temperature, humidity, and air quality are connected to the control unit by electrical wires. As a result of analytical studies of the automatic ventilation system for polluted air intake from a pigsty, the conditions for its effective operation have been mathematically substantiated. The developed technique and the algorithm implemented based on the Mathematica software package allows calculating the area of holes that form intake dampers with servomechanisms in the air intake pipes. The distribution of velocities in the air intake pipes and the distribution diagram of the area of holes that form intake dampers with servomechanisms in the air intake pipes are determined taking into account the design and technological parameters of the ventilation system and the distribution of the gas concentration (carbon dioxide, ammonia, and hydrogen sulphide) over the pens