Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - Scopus: 9A Dynamical and Sensitivity Analysis of the Caputo Fractional-Order Ebola Virus Model: Implications for Control Measures(Thammasat University, 2023) Ahmed, I.; Jarad, Fahd; Yusuf, A.; Tariboon, J.; Muhammad, M.; Jarad, F.; Mikailu, B.B.; MatematikThe recurrence of outbreaks in cases of Ebola virus among African countries remains one of the greatest issues of concern. Practices such as hunting or consumption of contam-inated bush meat, unsafe funeral practices, and environmental contamination have all been implicated as possible contributors. This paper investigates the transmission dynamics of the Ebola virus model in the setting of a Caputo fractional-order derivative that accounts for both direct and indirect transmissions of the virus. By employing the concept of fixed theorems, we derived the existence and uniqueness results of the model. Moreover, we analyzed the forward normalized sensitivity indices to identify the critical parameters for controlling the infection and found that reducing the contact rate between infected individuals and susceptible vectors is vital to limiting the virus’s spread. Comparing the proposed fractional-order model with those of the previously developed integer-order model numerically, we found that the proposed model provides more reliable information on the model’s dynamics. Thus, we conclude that the Caputo fractional-order operator is a precise tool for describing the proposed model behavior and can help understand the complexities of Ebola virus disease outbreaks. © 2023, Thammasat University. All rights reserved.Article 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: 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.Book Part Citation - Scopus: 14Fractional Differential Equations With Bio-Medical Applications(De Gruyter, 2019) Baleanu, D.; Tang, Y.; Arshad, S.In this chapter, we investigate the dynamics of fractional order models in bio-medical. First, we examine the fractional order model of HIV Infection and analyze the stability results for non-infected and infected equilibrium points. Then, we concentrate on the fractional order tumor growth model and establish a sufficient condition for existence and uniqueness of the solution of the fractional order tumor growth model. Local stability of the four equilibrium points of the model, namely the tumor free equilibrium, the dead equilibrium of type 1, the dead equilibrium of type 2 and the coexisting equilibrium is investigated by applying Matignons condition. Dynamics of the fractional order tumor model is numerically investigated by varying the fractional-order parameter and the system parameters. © 2019 Walter de Gruyter GmbH, Berlin/Boston.Article Citation - WoS: 15Citation - Scopus: 14Comparative Analysis of Fractional Order Dengue Model With Temperature Effect Via Singular and Non-Singular Operators(Pergamon-elsevier Science Ltd, 2021) Defterli, OzlemIn this work, we generalize a (deterministic) mathematical model that anticipates the influence of temperature on dengue transmission incorporating temperature-dependent model parameters. The motivation comes by the epidemiological evidence and several recent studies clearly states fluctuations in temperature, rainfall, and global climate indexes are determinant on the transmission dynamic and epidemic behavior of dengue virus that causes deadly diseases with incidence rates significantly risen worldwide in the past decade. Taking into account the importance of the subject in nowadays and the diversity of fractional calculus operators in mathematical modeling of complex real-world systems, in this paper we investigated the importance of the new model based on Mittag-Leffler kernel as being non-singular kernel. The sensitivity analysis of the generalized model is newly investigated. Numerical simulations are carried out in a comparative sense within the temperature fluctuations for both singular and non-singular fractional operators of different orders. (c) 2021 Elsevier Ltd. All rights reserved.Article Citation - WoS: 32Citation - Scopus: 30Analysis of the Fractional Corona Virus Pandemic Via Deterministic Modeling(Wiley, 2021) Tri, Vo Viet; Baleanu, Dumitru; Tuan, Nguyen HuyWith every passing day, one comes to know that cases of the corona virus disease are increasing. This is an alarming situation in many countries of the globe. So far, the virus has attacked as many as 188 countries of the world and 5 549 131 (27 May 2020) human population is affected with 348 224 deaths. In this regard, public and private health authorities are looking for manpower with modeling skills and possible vaccine. In this research paper, keeping in view the fast transmission dynamics of the virus, we have proposed a new mathematical model of eight mutually distinct compartments with the help of memory-possessing operator of Caputo type. The fractional order parameter psi of the model has been optimized so that smallest error can be attained while comparing simulations and the real data set which is considered for the country Pakistan. Using Banach fixed point analysis, it has been shown that the model has a unique solution whereas its basic reproduction numberR0is approximated to be 6.5894. Disease-free steady state is shown to be locally asymptotically stable forR0<0, otherwise unstable. Nelder-Mead optimization algorithm under MATLAB Toolbox with daily real cases of the virus in Pakistan is employed to obtain best fitted values of the parameters for the model's validation. Numerical simulations of the model have come into good agreement with the practical observations wherein social distancing, wearing masks, and staying home have proved to be the most effective measures in order to prevent the virus from further spread.Article Citation - WoS: 35Citation - Scopus: 38Efficiency of the New Fractional Derivative With Nonsingular Mittag-Leffler Kernel To Some Nonlinear Partial Differential Equations(Pergamon-elsevier Science Ltd, 2018) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, Abdullahi; Isa Aliyu, AliyuIn this work, the efficiency of the Atangana-Baleanu (AB) derivative over Caputo-Fabrizio (CF) to some nonlinear partial differential equation is presented. The considered equations are Rosenou-Haynam equation (RHE) and a class of mKdV (CmKdV) equation. The effective and efficient technique called the fractional homotopy perturbation transform method (FHPTM) is applied for the investigation of the governing equations. (C) 2018 Elsevier Ltd. All rights reserved.