scholarly journals Mathematical model of survival of fractional calculus, critics and their impact: How singular is our world?

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Abdon Atangana
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lyapunov Function ◽  
Fractional Calculus ◽  
Reproductive Number ◽  
Second Derivative ◽  
Suggested Model ◽  
Stochastic Version ◽  
The Past ◽  
Elementary Analysis

AbstractFractional calculus as was predicted by Leibniz to be a paradox, has nowadays evolved to become a centre of interest for many researchers from various backgrounds. As a result, multiple innovative ideas had emerged, which caused significant divisions regarding fractional calculus in the past three years. Therefore, this work is aimed at developing a mathematical model that could be used to depict the survival of fractional calculus. Six classes are herein considered to construct a mathematical model with six ordinary differential equations. All elementary analysis have been performed. Additionally, a new analysis including strength number that accounts for the accelerative information of nonlinear and linear parts of a given epidemiological model is introduced. An analysis of the second derivative of the Lyapunov function as well as an analysis of the second derivative of each class is applied to assess how a wave could be detected. It is strongly believed that this new analysis will particularly open new doors within the field of epidemiological modelling, which will aid researchers to better understand the spread of infectious diseases. The stochastic version of the suggested model was also investigated, and numerical simulations were performed. The obtained reproductive number, strength number, extinction of criticism together with numerical simulation, revealed that the field of fractional calculus will be stable will therefore have no significant effect soon.

scholarly journals Mathematical Model for Impact of Media on Cleanliness Drive in India

2018 ◽  
Vol 7 (1) ◽  
pp. 29-36
Author(s):  
N H Shah ◽  
J S Patel ◽  
F A Thakkar ◽  
M H Satia
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lyapunov Function ◽  
Global Stability ◽  
Transfer Rate ◽  
Equilibrium Points ◽  
Endemic Equilibrium ◽  
Local And Global Stability

A mathematical model on cleanliness drive in India is analysed for active cleaners and passive cleaners. Cleanliness and endemic equilibrium points are found. Local and global stability of these equilibrium points are discussed using Routh-Hurwitz criteria and Lyapunov function respectively. Impact of media (as a control) is studied on passive cleaners to become active. Numerical simulation of the model is carried out which indicates that with the help of media transfer rate to active cleaners from passive cleaners is higher.

scholarly journals Simpson’s Integral Inequalities for Twice Differentiable Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-15 ◽  
Author(s):  
Miguel Vivas-Cortez ◽  
Thabet Abdeljawad ◽  
Pshtiwan Othman Mohammed ◽  
Yenny Rangel-Oliveros
Keyword(s):  
Mathematical Model ◽  
Fractional Calculus ◽  
Mathematical Analysis ◽  
Integral Inequality ◽  
Special Functions ◽  
Quasiconvex Functions ◽  
Second Derivative ◽  
Integral Type ◽  
Research Article ◽  
New Inequalities

Integral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In the present research article, we obtain new inequalities of Simpson’s integral type based on the φ-convex and φ-quasiconvex functions in the second derivative sense. In the last sections, some applications on special functions are provided and shown via two figures to demonstrate the explanation of the readers.

scholarly journals Stability Analysis of Predator-Prey System with Fuzzy Impulsive Control

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yuangan Wang
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lyapunov Method ◽  
Impulsive Control ◽  
Control Model ◽  
Predator Prey ◽  
The Past ◽  
Prey System ◽  
S Model ◽  
Takagi Sugeno

Having attracted much attention in the past few years, predator-prey system provides a good mathematical model to present the correlation between predators and preys. This paper focuses on the robust stability of Lotka-Volterra predator-prey system with the fuzzy impulsive control model, and Takagi-Sugeno (T-S) fuzzy impulsive control model as well. Via the T-S model and the Lyapunov method, the controlling conditions of the asymptotical stability and exponential stability are established. Furthermore, the numerical simulation for the Lotka-Volterra predator-prey system with impulsive effects verifies the effectiveness of the proposed methods.

A prey - partially dependent predator with a reserved zone: modelling and analysis

2015 ◽  
Vol 5 (1) ◽  
pp. 1
Author(s):  
M.V. Ramana Murthy ◽  
Dahlia Khaled
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Lyapunov Function ◽  
Functional Response ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
The Other ◽  
Local Bifurcation ◽  
Control Parameters ◽  
Persistence Conditions

<p>In this paper, a mathematical model consisting of a prey-partially dependent predator has been proposed and analyzed. It is assumed that the prey moving between two types of zones, one is assumed to be a free hunting zone that is known as an unreserved zone and the other is a reserved zone where hunting is prohibited. The predator consumes the prey according to the Beddington-DeAngelis type of functional response. The existence, uniqueness and boundedness of the solution of the system are discussed. The dynamical behavior of the system has been investigated locally as well as globally with the help of Lyapunov function. The persistence conditions of the system are established. Local bifurcation near the equilibrium points has been investigated. Finally, numerical simulation has been used to specify the control parameters and confirm the obtained results.</p>

Numerical Simulation on Mold Electromagnetic Eccentric Stirring and Central Segregation of Round Bloom

2013 ◽  
Vol 652-654 ◽  
pp. 2450-2454
Author(s):  
Zhi Hong Zhang ◽  
Guo Guang Cheng
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Electromagnetic Stirring ◽  
Center Line ◽  
Central Segregation

The paper describes multi-section round bloom casting using external MEMS, equipped with max section D600mm and min D280mm mold, the center line of D280mm mold not coincident with the axis of stirrer coils. it is exist eccentric electromagnetic stirring of mold which section less than max D600mm, a mathematical model of MEMS has been established, the index of central segregation of D280mm macrostructure had decreased less than 1.12 by optimized parameters of electromagnetic stirring and SEN immerse depth, in the end, the quality of round bloom had improved.

Stability Analysis of an SEIR Epidemic Model with Stochastic Perturbation and Numerical Simulation

2013 ◽  
Vol 14 (2) ◽  
Author(s):  
Xiaoming Fan ◽  
Zhigang Wang
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Behavior ◽  
Epidemic Model ◽  
Reproduction Number ◽  
Stochastic Perturbation ◽  
Random Fluctuation ◽  
Deterministic System ◽  
Stochastic Version ◽  
Special Case ◽  
The Basic Reproduction Number

AbstractAn SEIR epidemic model with constant immigration and random fluctuation around the endemic equilibrium is considered. As a special case, a deterministic system discussed by Li et al. will be incorporated into the stochastic version given by us. We carry out a detailed analysis on the asymptotic behavior of the stochastic model, also regarding of the basic reproduction number ℛ

Numerical modelling of swirling momentumless turbulent wake dynamics

2018 ◽  
pp. 37-48
Author(s):  
Андрей Геннадьевич Деменков ◽  
Геннадий Георгиевич Черных
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Equations Of Motion ◽  
Turbulent Wake ◽  
The Body ◽  
Jet Flows ◽  
Reynolds Stresses ◽  
Bodies Of Revolution ◽  
Averaged Equations

С применением математической модели, включающей осредненные уравнения движения и дифференциальные уравнения переноса нормальных рейнольдсовых напряжений и скорости диссипации, выполнено численное моделирование эволюции безымпульсного закрученного турбулентного следа с ненулевым моментом количества движения за телом вращения. Получено, что начиная с расстояний порядка 1000 диаметров от тела течение становится автомодельным. На основе анализа результатов численных экспериментов построены упрощенные математические модели дальнего следа. Swirling turbulent jet flows are of interest in connection with the design and development of various energy and chemical-technological devices as well as both study of flow around bodies and solving problems of environmental hydrodynamics, etc. An interesting example of such a flow is a swirling turbulent wake behind bodies of revolution. Analysis of the known works on the numerical simulation of swirling turbulent wakes behind bodies of revolution indicates lack of knowledge on the dynamics of the momentumless swirling turbulent wake. A special case of the motion of a body with a propulsor whose thrust compensates the swirl is studied, but there is a nonzero integral swirl in the flow. In previous works with the participation of the authors, a numerical simulation of the initial stage of the evolution of a swirling momentumless turbulent wake based on a hierarchy of second-order mathematical models was performed. It is shown that a satisfactory agreement of the results of calculations with the available experimental data is possible only with the use of a mathematical model that includes the averaged equations of motion and differential equations for the transfer of normal Reynolds stresses along the rate of dissipation. In the present work, based on the above mentioned mathematical model, a numerical simulation of the evolution of a far momentumless swirling turbulent wake with a nonzero angular momentum behind the body of revolution is performed. It is shown that starting from distances of the order of 1000 diameters from the body the flow becomes self-similar. Based on the analysis of the results of numerical experiments, simplified mathematical models of the far wake are constructed. The authors dedicate this work to the blessed memory of Vladimir Alekseevich Kostomakha.

MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

2021 ◽  
Vol 5 (10) ◽  
Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
The Mathematical Model ◽  
Globally Stable ◽  
Well Posed ◽  
The Basic Reproduction Number ◽  
Invariant Principle

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

Design of Digital Filter Based on Numerical Simulation

2014 ◽  
Vol 539 ◽  
pp. 79-83
Author(s):  
Chuan Ting Wei ◽  
Quan Li Ning ◽  
Dong Chen
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Digital Filter ◽  
Sampling Frequency ◽  
New Wave ◽  
Matlab Software ◽  
Frequency Wave

In MATLAB software, it has FDATool toolbox, which can design digital filter specific according to specific circuit, and analyze the performance of the filter according to the parameters of filter. In this paper we establish simulation mathematical model of digital filter based on the calculation principle of distributed multiplication accumulator. According to the logic algorithm we design delay algorithm of digital filter, and use MATLAB software to do simulation on amplitude frequency and phase frequency of digital filter. After superposition of different sampling frequency wave we get new waveform, and realize the digital filter for the new wave. It proves the availability of mathematical model and the program, and provides the technical reference for the design of digital filter.

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