Differentıal Transform Method for Solvıng a Boundary Value Problem Arısıng in Chemıcal Reactor Theory

In this study, we deal with the numerical solution of the mathematical model for an adiabatic tubular chemical reactor which processes an irreversible exothermic chemical reaction. For steady state solutions, the model can be reduced to the following nonlinear ordinary differential equation [1]: (1) where lambda, mu and beta are Péclet number, Damköhler number and adiabatic temperature rise, respectively. Boundary conditions of Eq. (1) are (2) Differential transform method [2] is used to solve the problem (1)-(2) for some values of the considered parameters. Residual error computation is adopted to confirm the accuracy of the results. In addition, the obtained results are compared with those obtained by other existing numerical approach [3]

A new fractional mathematical modelling of COVID-19 with the availability of vaccine

[EN] The most dangerous disease of this decade novel coronavirus or COVID-19 is yet not over. The whole world is facing this threat and trying to stand together to defeat this pandemic. Many countries have defeated this virus by their strong control strategies and many are still trying to do so. To date, some countries have prepared a vaccine against this virus but not in an enough amount. In this research article, we proposed a new SEIRS dynamical model by including the vaccine rate. First we formulate the model with integer order and after that we generalize it in Atangana-Baleanu derivative sense. The high motivation to apply Atangana-Baleanu fractional derivative on our model is to explore the dynamics of the model more clearly. We provide the analysis of the existence of solution for the given fractional SEIRS model. We use the famous Predictor-Corrector algorithm to derive the solution of the model. Also, the analysis for the stability of the given algorithm is established. We simulate number of graphs to see the role of vaccine on the dynamics of the population. For practical simulations, we use the parameter values which are based on real data of Spain. The main motivation or aim of this research study is to justify the role of vaccine in this tough time of COVID-19. A clear role of vaccine at this crucial time can be realized by this study.The third author is supported by MEC, Spain, grants MTM2016-75963-P and PID2019105011GBI00Kumar, P.; Erturk, VS.; Murillo Arcila, M. (2021). A new fractional mathematical modelling of COVID-19 with the availability of vaccine. Results in Physics. 24:1-26. https://doi.org/10.1016/j.rinp.2021.1042131262

Design, Performance, and Calibration of the CMS Hadron-Outer Calorimeter

The CMS hadron calorimeter is a sampling calorimeter with brass absorber and plastic scintillator tiles with wavelength shifting fibres for carrying the light to the readout device. The barrel hadron calorimeter is complemented with an outer calorimeter to ensure high energy shower containment in the calorimeter. Fabrication, testing and calibration of the outer hadron calorimeter are carried out keeping in mind its importance in the energy measurement of jets in view of linearity and resolution. It will provide a net improvement in missing \et measurements at LHC energies. The outer hadron calorimeter will also be used for the muon trigger in coincidence with other muon chambers in CMS

A complex fractional mathematical modeling for the love story of Layla and Majnun

[EN] In this article, we provide numerical simulations to show the importance and the effects of fractional order derivatives in psychological studies. As it is well-known, complex variables are more realistic for defining structures in different cases. In this paper, we evidence that such dynamics become more realistic when we use fractional derivatives. We study a non-integer order, non-linear mathematical model for defining a love story of Layla and Majnun (a couple in a romantic relationship). We exemplify all necessary practical calculations to study this serious psychological phenomena. The existence of the unique solution for the given model is exhibited. We use a very recent and strong modified Predictor-Corrector algorithm to evaluate the model structure. Stability of the proposed method is also given. We exemplify that the given complex fractional model is more realistic and represents reality more closely. The proposed model is very basic, significant, and efficient at introducing distinct natures by only replacing one control parameter. In this study, we found that in some of the cases there are stable limit cycles, in some cases periodic behaviours and sometimes transiently chaotic solutions exist which cannot be observed for integer order models at same parameter values. The principal contribution of this article is to exhibit the importance of non-integer order derivatives for analysing complex dynamics. The use of complex variables makes this study more effective because they have both magnitude and phase to better explore the love and can describe different emotions such as coexisting love and hate. (c) 2021 Elsevier Ltd. All rights reserved.Kumar, P.; Erturk, VS.; Murillo Arcila, M. (2021). A complex fractional mathematical modeling for the love story of Layla and Majnun. Chaos, Solitons and Fractals. 150:1-11. https://doi.org/10.1016/j.chaos.2021.111091S11115

The differential transform method and Pade approximants for a fractional population growth model

WOS: 000310411700006Purpose - The purpose of this paper is to propose an approximate method for solving a fractional population growth model in a closed system. The fractional derivatives are described in the Caputo sense. Design/methodology/approach - The approach is based on the differential transform method. The solutions of a fractional model equation are calculated in the form of convergent series with easily computable components. Findings - The diagonal Pade approximants are effectively used in the analysis to capture the essential behavior of the solution. Originality/value - Illustrative examples are included to demonstrate the validity and applicability of the technique

Mathematical Model for Coronavirus Disease 2019 (COVID-19) Containing Isolation Class

The deadly coronavirus continues to spread across the globe, and mathematical models can be used to show suspected, recovered, and deceased coronavirus patients, as well as how many people have been tested. Researchers still do not know definitively whether surviving a COVID-19 infection means you gain long-lasting immunity and, if so, for how long? In order to understand, we think that this study may lead to better guessing the spread of this pandemic in future. We develop a mathematical model to present the dynamical behavior of COVID-19 infection by incorporating isolation class. First, the formulation of model is proposed; then, positivity of the model is discussed. The local stability and global stability of proposed model are presented, which depended on the basic reproductive. For the numerical solution of the proposed model, the nonstandard finite difference (NSFD) scheme and Runge-Kutta fourth order method are used. Finally, some graphical results are presented. Our findings show that human to human contact is the potential cause of outbreaks of COVID-19. Therefore, isolation of the infected human overall can reduce the risk of future COVID-19 spread

Fractional mathematical modeling of the Stuxnet virus along with an optimal control problem

In this digital, internet-based world, it is not new to face cyber attacks from time to time. A number of heavy viruses have been made by hackers, and they have successfully given big losses to our systems. In the family of these viruses, the Stuxnet virus is a well-known name. Stuxnet is a very dangerous virus that probably targets the control systems of our industry. The main source of this virus can be an infected USB drive or flash drive. In this research paper, we study a mathematical model to define the dynamical structure or the effects of the Stuxnet virus on our computer systems. To study the given dynamics, we use a modified version of the Caputo-type fractional derivative, which can be used as an old Caputo derivative by fixing some slight changes, which is an advantage of this study. We demonstrate that the given fractional Caputo-type dynamical model has a unique solution using fixed point theory. We derive the solution of the proposed non-linear non-classical model with the application of a recent version of the Predictor–Corrector scheme. We analyze various graphs at different values of the arrival rate of new computers, damage rate, virus transmission rate, and natural removal rate. In the graphical interpretations, we verify the values of fractional orders and simulate 2-D and 3-D graphics to understand the dynamics clearly. The major novelty of this study is that we formulate the optimal control problem and its important consequences both theoretically and mathematically, which can be further extended graphically. The main contribution of this research work is to provide some novel results on the Stuxnet virus dynamics and explore the uses of fractional derivatives in computer science. The given methodology is effective, fully novel, and very easy to understand

A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives

[EN] In this study, our aim is to explore the dynamics of COVID-19 or 2019-nCOV in Argentina considering the parameter values based on the real data of this virus from March 03, 2020 to March 29, 2021 which is a data range of more than one complete year. We propose a Atangana-Baleanu type fractional-order model and simulate it by using predictor-corrector (P-C) method. First we introduce the biological nature of this virus in theoretical way and then formulate a mathematical model to define its dynamics. We use a well-known effective optimization scheme based on the renowned trust-region-reflective (TRR) method to perform the model calibration. We have plotted the real cases of COVID-19 and compared our integer-order model with the simulated data along with the calculation of basic reproductive number. Concerning fractional-order simulations, first we prove the existence and uniqueness of solution and then write the solution along with the stability of the given P-C method. A number of graphs at various fractional-order values are simulated to predict the future dynamics of the virus in Argentina which is the main contribution of this paper.The third author is supported by MICINN and FEDER, Project PID2019-105011GB-I00.Kumar, P.; Erturk, VS.; Murillo Arcila, M.; Banerjee, R.; Manickam, A. (2021). A case study of 2019-nCOV cases in Argentina with the real data based on daily cases from March 03, 2020 to March 29, 2021 using classical and fractional derivatives. Advances in Difference Equations. 2021(1):1-21. https://doi.org/10.1186/s13662-021-03499-2S1212021

Evaluation of dentin permeability of fluorotic permanent teeth

Objective: The in vitro permeability characteristics of dentin have been studied extensively and used to evaluate the efficacy of various preventative and restorative procedures. The aim of this in vitro study was to precisely determine the dentin permeability of fluorotic premolar teeth using an electronic hydraulic conductance measurement system with photosensors and to compare the data with healthy premolars