Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 50Citation - Scopus: 55Numerical Analysis of Atangana-Baleanu Fractional Model To Understand the Propagation of a Novel Corona Virus Pandemic(Elsevier, 2022) Butt, A. I. K.; Ahmad, W.; Rafiq, M.; Baleanu, D.In this manuscript, we formulated a new nonlinear SEIQR fractional order pandemic model for the Corona virus disease (COVID-19) with Atangana-Baleanu derivative. Two main equilibrium points F-0*, F-1* of the proposed model are stated. Threshold parameter R-0 for the model using next generation technique is computed to investigate the future dynamics of the disease. The existence and uniqueness of solution is proved using a fixed point theorem. For the numerical solution of fractional model, we implemented a newly proposed Toufik-Atangana numerical scheme to validate the importance of arbitrary order derivative q and our obtained theoretical results. It is worth mentioning that fractional order derivative provides much deeper information about the complex dynamics of Corona model. Results obtained through the proposed scheme are dynamically consistent and good in agreement with the analytical results. To draw our conclusions, we explore a complete quantitative analysis of the given model for different quarantine levels. It is claimed through numerical simulations that pandemic could be eradicated faster if a human community selfishly adopts mandatory quarantine measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effectiveness of quarantine policy on human population. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).Article Citation - WoS: 7Citation - Scopus: 7A Peculiar Application of the Fractal-Fractional Derivative in the Dynamics of a Nonlinear Scabies Model(Elsevier, 2022) Kanwal, Bushra; Jarad, Fahd; Elagan, S. K.; Rashid, SaimaIn this paper, we provide a generic mathematical framework for scabies transmission mechanisms. The infections involving susceptible, highly contagious people and juvenile scabiei mites are characterized by a framework of ordinary differential equations (DEs). The objective of this study is to examine the evolution of scabies disease employing a revolutionary configuration termed a fractal-fractional (FF) Atangana-Baleanu (AB) operator. Generic dynamical estimates are used to simulate the underlying pace of growth of vulnerable people, clinical outcomes, and also the eradication and propagation rates of contaminated people and immature mites. We study and comprehend our system, focusing on a variety of restrictions on its basic functionalities. The model's outcomes are assessed for positivity and boundedness. The formula includes a fundamental reproducing factor, R-0, that ensures the presence and stability of all relevant states. Furthermore, the FF-AB operator is employed in the scabies model, and its mathematical formulation is presented using a novel process. We analyze the FF framework to construct various fractal and fractional levels and conclude that the FF theory predicts the affected occurrences of scabies illness adequately. The relevance and usefulness of the recently described operator has been demonstrated through simulations of various patterns of fractal and fractional data.Article Citation - WoS: 34Citation - Scopus: 43Study of Global Dynamics of Covid-19 Via a New Mathematical Model(Elsevier, 2020) Seadawy, Aly R.; Shah, Kamal; Ullah, Aman; Baleanu, Dumitru; Din, Rahim UdThe theme of this paper focuses on the mathematical modeling and transmission mechanism of the new Coronavirus shortly noted as (COVID-19), endangering the lives of people and causing a great menace to the world recently. We used a new type epidemic model composed on four compartments that is susceptible, exposed, infected and recovered (SEIR), which describes the dynamics of COVID-19 under convex incidence rate. We simulate the results by using nonstandard finite difference method (NSFDS) which is a powerful numerical tool. We describe the new model on some random data and then by the available data of a particular regions of Subcontinents.Article Citation - WoS: 25Citation - Scopus: 25Stability Data Dependency and Errors Estimation for a General Iteration Method(Elsevier, 2021) Ali, Danish; Karapinar, Erdal; Hussain, AftabIn this paper, we present a result of stability, data Dependency and errors estimation for D Iteration Method. We also prove that errors in D iterative process is controllable. Especially stability, data dependence, controllability, error accumulation of such iterative methods are being studied. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.Article Citation - WoS: 196Citation - Scopus: 199Impulsive Effects on Stability and Passivity Analysis of Memristor-Based Fractional-Order Competitive Neural Networks(Elsevier, 2020) Chanthorn, P.; Niezabitowski, M.; Raja, R.; Baleanu, D.; Pratap, A.; Rajchakit, G.This paper analyzes the stability and passivity problems for a class of memristor-based fractional-order competitive neural networks (MBFOCNNs) by using Caputo's fractional derivation. Firstly, impulsive effects are taken well into account and effective analysis techniques are used to reflect the system's practically dynamic behavior. Secondly, by using the Lyapunov technique, some sufficient conditions are obtained by linear matrix inequalities (LMIs) to ensure the stability and passivity of the MBFOCNNs, which can be effectively solved by the LMI computational tool in MATLAB. Finally, two numerical models and their simulation results are given to illustrate the effectiveness of the proposed results. (C) 2020 Elsevier B.V. All rights reserved.Article Impulsive effects on stability and passivity analysis of memristor-based fractional-order competitive neural networks(Elsevier, 2020) Rajchakit, G.; Chanthorn, P.; Niezabitowski, M.; Raja, R.; Baleanu, Dumitru; Pratap, A.This paper analyzes the stability and passivity problems for a class of memristor-based fractional-order competitive neural networks (MBFOCNNs) by using Caputo's fractional derivation. Firstly, impulsive effects are taken well into account and effective analysis techniques are used to reflect the system's practically dynamic behavior. Secondly, by using the Lyapunov technique, some sufficient conditions are obtained by linear matrix inequalities (LMIs) to ensure the stability and passivity of the MBFOCNNs, which can be effectively solved by the LMI computational tool in MATLAB. Finally, two numerical models and their simulation results are given to illustrate the effectiveness of the proposed results. © 2020 Elsevier B.V.Article Citation - WoS: 37Citation - Scopus: 43Stable Numerical Results To a Class of Time-Space Fractional Partial Differential Equations Via Spectral Method(Elsevier, 2020) Abdeljawad, Thabet; Shah, Kamal; Jarad, FahdIn this paper, we are concerned with finding numerical solutions to the class of time-space fractional partial differential equations: D(t)(p)u(t, x) + kappa D(x)(p)u(t, x) + tau u(t, x) = g(t, x), 1 < p < 2, (t, x) is an element of [0,1] x [0, 1], under the initial conditions. u(0, x) = theta(x), u(t)(0, x) = phi(x), and the mixed boundary conditions. u(t, 0) = u(x)(t, 0) = 0, where D-t(p) is the arbitrary derivative in Caputo sense of order p corresponding to the variable time t. Further, D-x(p) is the arbitrary derivative in Caputo sense with order p corresponding to the variable space x. Using shifted Jacobin polynomial basis and via some operational matrices of fractional order integration and differentiation, the considered problem is reduced to solve a system of linear equations. The used method doesn't need discretization. A test problem is presented in order to validate the method. Moreover, it is shown by some numerical tests that the suggested method is stable with respect to a small perturbation of the source data g(t, x). Further the exact and numerical solutions are compared via 3D graphs which shows that both the solutions coincides very well. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.