Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Numerical Simulation of Drag Reduction on a Square Rod Detached with Two Control Rods at Various Gap Spacing via Lattice Boltzmann Method(MDPI AG, 2020) Baleanu, Dumitru; Khalid, Asma; Nisar, Kottakkaran Sooppy; Khan, Ilyas; Islam, Shams-Ul; Manzoor, RaheelaArticle Citation - WoS: 24Citation - Scopus: 23Spatio-Temporal Numerical Modeling of Auto-Catalytic Brusselator Model(Editura Acad Romane, 2019) Ahmed, Nauman; Baleanu, Dumitru; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-Ur; Aziz-Ur Rehman, Muhammad; MatematikThe main objective of this article is to propose a chaos free explicit finite-difference (FD) scheme to find the numerical solution for the Brusselator reaction-diffusion model. The scheme is unconditionally stable and it is unconditionally dynamically consistent with the positivity property of continuous model as unknown quantities of auto-catalytic Brusselator system describe the concentrations of two reactant substances. Stability of the proposed FD method is showed with the help of Neumann criteria of stability. Taylor series is used to validate the consistency of the proposed FD method. Forward Euler explicit FD approach and semi-implicit Crank-Nicolson FD scheme are also applied to solve the Brusselator reaction-diffusion system and to make the comparison with the proposed FD scheme.Article Citation - WoS: 29Citation - Scopus: 21A New Fractional Infectious Disease Model Under the Non-Singular Mittag-Leffler Derivative(Taylor & Francis Ltd, 2022) Liu, Xuan; Ur Rahmamn, Mati; Ahmad, Saeed; Baleanu, Dumitru; Nadeem Anjam, YasirIn this manuscript, we consider a fractional mathematical model, which describes the dynamics of infectious disease, under the non-singular Mittag-Leffler derivative. The model under consideration is the extension of the SIRV model, where the infectious class has been divided into two compartments, namely the acute and chronically infectious individuals. First, we obtain the possible equilibrium states of the given model. With the help of the next generation matrix approach, the reproduction number has been calculated for the system to find conditions on the spread or control of the disease. Additionally, a new concept of strength number and analysis of the second derivative of the Lyapunov function has been used for the detection of waves. We investigate the said problem for qualitative analysis and determine at least one solution by applying the approach of fixed point theory. For approximate solution, the technique of iterative fractional-order Adams-Bashforth scheme has been used. Numerical simulation for the proposed scheme has been performed at various fractional-order lying between 0, 1 and for integer-order 1. All the compartments show convergency and stability with growing time. A good comparative result has been given by different fractional orders and achieves stability faster at the low fractional orders.Article Citation - WoS: 90Citation - Scopus: 95Existence of Solutions and a Numerical Scheme for a Generalized Hybrid Class of N-Coupled Modified Abc-Fractional Differential Equations With an Application(Amer inst Mathematical Sciences-aims, 2023) Baleanu, Dumitru; Alobaidi, Ghada; Rehman, Mutti-Ur; Khan, Hasib; Alzabut, JehadIn this article, we investigate some necessary and sufficient conditions required for the existence of solutions for mABC-fractional differential equations (mABC-FDEs) with initial conditions; additionally, a numerical scheme based on the the Lagrange's interpolation polynomial is established and applied to a dynamical system for the applications. We also study the uniqueness and Hyers-Ulam stability for the solutions of the presumed mABC-FDEs system. Such a system has not been studied for the mentioned mABC-operator and this work generalizes most of the results studied for the ABC operator. This study will provide a base to a large number of dynamical problems for the existence, uniqueness and numerical simulations. The results are compared with the classical results graphically to check the accuracy and applicability of the scheme.Article Citation - WoS: 44Citation - Scopus: 53On a New Conceptual Mathematical Model Dealing the Current Novel Coronavirus-19 Infectious Disease(Elsevier, 2020) Shah, Kamal; Seadawy, Aly; Alrabaiah, Hussam; Baleanu, Dumitru; Din, AnwarudThe present paper describes a three compartment mathematical model to study the transmission of the current infection due to the novel coronavirus (2019-nCoV or COVID-19). We investigate the aforesaid dynamical model by using Atangana, Baleanu and Caputo (ABC) derivative with arbitrary order. We derive some existence results together with stability of Hyers-Ulam type. Further for numerical simulations, we use Adams-Bashforth (AB) method with fractional differentiation. The mentioned method is a powerful tool to investigate nonlinear problems for their respective simulation. Some discussion and future remarks are also given.Article Citation - WoS: 28Citation - Scopus: 32New Applications Related To Covid-19(Elsevier, 2021) Ahmed, Nauman; Raza, Ali; Iqbal, Zafar; Rafiq, Muhammad; Baleanu, Dumitru; Rehman, Muhammad Aziz-ur; Akgul, AliAnalysis of mathematical models projected for COVID-19 presents in many valuable outputs. We analyze a model of differential equation related to Covid-19 in this paper. We use fractal-fractional derivatives in the proposed model. We analyze the equilibria of the model. We discuss the stability analysis in details. We apply very effective method to obtain the numerical results. We demonstrate our results by the numerical simulations.Article Citation - WoS: 17Citation - Scopus: 21Modeling the Transmission Dynamics of Delayed Pneumonia-Like Diseases With a Sensitivity of Parameters(Springer, 2021) Baleanu, Dumitru; Raza, Ali; Rafiq, Muhammad; Soori, Atif Hassan; Mohsin, Muhammad; Naveed, MuhammadPneumonia is a highly transmitted disease in children. According to the World Health Organization (WHO), the most affected regions include South Asia and sub-Saharan Africa. 15% deaths of children are due to pneumonia. In 2017, 0.88 million children were killed under the age of five years. An analysis of pneumonia disease is performed with the help of a delayed mathematical modelling technique. The epidemiological system contemplates subpopulations of susceptible, carriers, infected and recovered individuals, along with nonlinear interactions between the members of those subpopulations. The positivity and the boundedness of the ongoing problem for nonnegative initial data are thoroughly proved. The system possesses pneumonia-free and pneumonia existing equilibrium points, whose stability is studied rigorously. Moreover, the numerical simulations confirm the validity of these theoretical results.Article Citation - WoS: 75Citation - Scopus: 82Mathematical Modeling of Pine Wilt Disease With Caputo Fractional Operator(Pergamon-elsevier Science Ltd, 2021) Acay, Bahar; Mustapha, Umar Tasiu; Inc, Mustafa; Baleanu, Dumitru; Yusuf, AbdullahiIn this work, we investigate the transmission dynamics of pine wilt disease infection and developed a new model utilizing Caputo fractional-order derivative. Moreover, with the use of fixed point theorem, the existence and uniqueness of the pine wilt disease model are obtained under Caputo operator. Using forward normalized sensitivity index, we determine the most sensitive parameters essential for the control of the infection and the results show that, decreasing the values of contact rate of a susceptible vector with infected pine trees and progression rate play a significant role in controlling the spread of pine wilt disease infection. On the other hand, we obtain different numerical simulations results of the model using the appropriate parameter values. Hence, from the graphs, it can be concluded that Caputo fractional operator gives more biologically observable behavior of the proposed disease model thanks to the changed fractional order. Compared to the previously built integer order model, the non-integer order derivative provided more efficient and flexible information about the complexity of the model's dynamics. (c) 2020 Elsevier Ltd. All rights reserved.Article Citation - WoS: 17Citation - Scopus: 21Mathematical Modeling and Analysis of the Novel Coronavirus Using Atangana-Baleanu Derivative(Elsevier, 2021) El-Dessoky, M. M.; Baleanu, Dumitru; Alzahrani, EbraheemThe novel Coronavirus infection disease is becoming more complex for the humans society by giving death and infected cases throughout the world. Due to this infection, many countries of the world suffers from great economic loss. The researchers around the world are very active to make a plan and policy for its early eradication. The government officials have taken full action for the eradication of this virus using different possible control strategies. It is the first priority of the researchers to develop safe vaccine against this deadly disease to minimize the infection. Different approaches have been made in this regards for its elimination. In this study, we formulate a mathematical epidemic model to analyze the dynamical behavior and transmission patterns of this new pandemic. We consider the environmental viral concentration in the model to better study the disease incidence in a community. Initially, the model is constructed with the derivative of integer order. The classical epidemic model is then reconstructed with the fractional order operator in the form of Atangana-Baleanu derivative with the nonsingular and nonlocal kernel in order to analyze the dynamics of Coronavirus infection in a better way. A well-known estimation approach is used to estimate model parameters from the COVID-19 cases reported in Saudi Arabia from March 1 till August 20, 2020. After the procedure of parameters estimation, we explore some basic mathematical analysis of the fractional model. The stability results are provided for the disease free case using fractional stability concepts. Further, the uniqueness and existence results will be shown using the Picard-Lendelof approach. Moreover, an efficient numerical scheme has been proposed to obtain the solution of the model numerically. Finally, using the real fitted parameters, we depict many simulation results in order to demonstrate the importance of various model parameters and the memory index on disease dynamics and possible eradication.Article Citation - WoS: 26Citation - Scopus: 27Mathematical Analysis of Tuberculosis Control Model Using Nonsingular Kernel Type Caputo Derivative(Springer, 2021) Ullah, Rafi; Baleanu, Dumitru; Ahmad, SaeedThis research work investigates some theoretical and semi-analytical results for the mathematical model of tuberculosis disease via derivative due to Caputo and Fabrizio. The concerned derivative involves exponential kernel and very recently it has been adapted for various applied problems. The required results are established by using some fixed point approach of Krasnoselskii and Banach. Further, by the use of iterative tools of Adomian decomposition and Laplace, the semi-analytical results are studied. Some graphical results are given with discussion.