Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

Browse

Filters

2007 - 200912010 - 2019242020 - 20224

Settings

COAR Access Rights: search.filters.coarAccessRights.open accessPublisher: search.filters.publisher.Pergamon-elsevier Science Ltd

Search Results

Now showing 1 - 10 of 29
  • Correction
  • Editorial
    Citation - WoS: 1
    Citation - Scopus: 2
    Editorial: Recent Advances in Computational Biology
    (Pergamon-elsevier Science Ltd, 2022) Srivastava, Hari Mohan; Cattani, Carlo; Baleanu, Dumitru
  • Article
    Citation - WoS: 29
    Citation - Scopus: 39
    An Intuitionistic Fuzzy Decision Support System for Covid-19 Lockdown Relaxation Protocols in India
    (Pergamon-elsevier Science Ltd, 2022) Devi, S. Aicevarya; Felix, A.; Narayanamoorthy, Samayan; Ahmadian, Ali; Balaenu, Dumitru; Kang, Daekook; Aicevarya Devi, S.
    In January 2020, the World Health Organization (WHO) identified a world-threatening virus, SARS-CoV-2. To diminish the virus spread rate, India implemented a six-month-long lockdown. During this period, the Indian government lifted certain restrictions. Therefore, this study investigates the efficacy of India's lockdown relaxation protocols using fuzzy decision-making. The decision-making trial and evaluation laboratory (DEMATEL) is one of the fuzzy MCDM methods. When it is associated with intuitionistic fuzzy circumstances, it is known as the intuitionistic fuzzy DEMATEL (IF-DEMATEL) method. Moreover, converting intuitionistic fuzzy into a crisp score (CIFCS) algorithm is an aggregation technique utilized for the intuitionistic fuzzy set. By using IF-DEMATEL and CIFCS, the most efficient lockdown relaxation protocols for COVID-19 are determined. It also provides the cause and effect relationship of the lockdown relaxation protocols. Additionally, the comparative study is carried out through various DEMATEL methods to see the effectiveness of the result. The findings would be helpful to the government's decision-making process in the fight against the pandemic.
  • Article
    Citation - WoS: 102
    Citation - Scopus: 111
    Stationary Distribution and Extinction of Stochastic Coronavirus (covid-19) Epidemic Model
    (Pergamon-elsevier Science Ltd, 2020) Khan, Amir; Baleanu, Dumitru; Din, Anwarud
    Similar to other epidemics, the novel coronavirus (COVID-19) spread very fast and infected almost two hundreds countries around the globe since December 2019. The unique characteristics of the COVID-19 include its ability of faster expansion through freely existed viruses or air molecules in the atmosphere. Assuming that the spread of virus follows a random process instead of deterministic. The continuous time Markov Chain (CTMC) through stochastic model approach has been utilized for predicting the impending states with the use of random variables. The proposed study is devoted to investigate a model consist of three exclusive compartments. The first class includes white nose based transmission rate (termed as susceptible individuals), the second one pertains to the infected population having the same perturbation occurrence and the last one isolated (quarantined) individuals. We discuss the model's extinction as well as the stationary distribution in order to derive the the sufficient criterion for the persistence and disease' extinction. Lastly, the numerical simulation is executed for supporting the theoretical findings. (C) 2020 Published by Elsevier Ltd.
  • Article
    Citation - WoS: 28
    Citation - Scopus: 30
    Asymptotic Integration of (1+α)-Order Fractional Differential Equations
    (Pergamon-elsevier Science Ltd, 2011) Mustafa, Octavian G.; Agarwal, Ravi P.; Baleanu, Dumitru
    We establish the long-time asymptotic formula of solutions to the (1 + alpha)-order fractional differential equation (i)(0)O(t)(1+alpha)x + a (t)x = 0, t > 0, under some simple restrictions on the functional coefficient a(t), where (i)(0)O(t)(1+alpha)x is one of the fractional differential operators D-0(t)alpha(x'), ((0)D(t)(alpha)x)' = D-0(t)1+alpha x and D-0(t)alpha(tx' - x). Here, D-0(t)alpha designates the Riemann-Liouville derivative of order a E (0, 1). The asymptotic formula reads as [b + O(1)] . x(small) + c . x(large) as t -> +infinity for given b, c E is an element of R, where x(small) and x(large) represent the eventually small and eventually large solutions that generate the solution space of the fractional differential equation (i)(0)O(t)(1+alpha)x = 0, t > 0. (C) 2011 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 29
    Citation - Scopus: 30
    A Mathematical Model of the Evolution and Spread of Pathogenic Coronaviruses From Natural Host To Human Host
    (Pergamon-elsevier Science Ltd, 2020) Baleanu, Dumitru; Alzabut, Jehad; Bozkurt, Fatma; Yousef, Ali
    Coronaviruses are highly transmissible and are pathogenic viruses of the 21st century worldwide. In general, these viruses are originated in bats or rodents. At the same time, the transmission of the infection to the human host is caused by domestic animals that represent in the habitat the intermediate host. In this study, we review the currently collected information about coronaviruses and establish a model of differential equations with piecewise constant arguments to discuss the spread of the infection from the natural host to the intermediate, and from them to the human host, while we focus on the potential spillover of bat-borne coronaviruses. The local stability of the positive equilibrium point of the model is considered via the Linearized Stability Theorem. Besides, we discuss global stability by employing an appropriate Lyapunov function. To analyze the outbreak in early detection, we incorporate the Allee effect at time t and obtain stability conditions for the dynamical behavior. Furthermore, it is shown that the model demonstrates the Neimark-Sacker Bifurcation. Finally, we conduct numerical simulations to support the theoretical findings. (C) 2020 Elsevier Ltd. All rights reserved.
  • Editorial
    Citation - WoS: 4
    Citation - Scopus: 4
    Fractional Differentiation and Its Applications I
    (Pergamon-elsevier Science Ltd, 2013) Tenreiro Machado, J. A.; Chen, Wen; Baleanu, Dumitru
  • Article
    Citation - WoS: 24
    Citation - Scopus: 31
    A Note on Stability of Sliding Mode Dynamics in Suppression of Fractional-Order Chaotic Systems
    (Pergamon-elsevier Science Ltd, 2013) Delavari, Hadi; Baleanu, Dumitru; Faieghi, Mohammad Reza
    We consider a class of fractional-order chaotic systems which undergoes unknown perturbations. We revisit the problem of sliding mode controller design for robust stabilization of chaotic systems using one control input. In the recent works, it was assumed that one of the system equations are perturbed by uncertainties. For this case we show that the sliding mode dynamics are globally stable which is not addressed so far. Next, we allow that all the system's equations depend on uncertain terms and provide a theoretical justification for applicability of the existing design. We also determine the least amount of precise information about the chaotic system that is needed to design the controller. (C) 2012 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 134
    Citation - Scopus: 160
    A New Approach for Solving a System of Fractional Partial Differential Equations
    (Pergamon-elsevier Science Ltd, 2013) Nazari, M.; Baleanu, D.; Khalique, C. M.; Jafari, H.
    In this paper we propose a new method for solving systems of linear and nonlinear fractional partial differential equations. This method is a combination of the Laplace transform method and the Iterative method and here after called the Iterative Laplace transform method. This method gives solutions without any discretization and restrictive assumptions. The method is free from round-off errors and as a result the numerical computations are reduced. The fractional derivative is described in the Caputo sense. Finally, numerical examples are presented to illustrate the preciseness and effectiveness of the new technique. (C) 2012 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 29
    Citation - Scopus: 33
    A Mathematical Model for Simulation of a Water Table Profile Between Two Parallel Subsurface Drains Using Fractional Derivatives
    (Pergamon-elsevier Science Ltd, 2013) Naseri, Abd Ali; Jafari, Hossein; Ghanbarzadeh, Afshin; Baleanu, Dumitru; Mehdinejadiani, Behrouz
    By considering the initial and boundary conditions corresponding to parallel subsurface drains, the linear form of a one-dimensional fractional Boussinesq equation was solved and an analytical mathematical model was developed to predict the water table profile between two parallel subsurface drains. The developed model is a generalization of the Glover-Dumm's mathematical model. As a result, the new model is applicable for both homogeneous and heterogeneous soils. It considers the degree of heterogeneity of soil as a determinable parameter. This parameter was called the heterogeneity index. The laboratory and field tests were conducted to study the performance of the proposed mathematical model in a homogenous soil and in an agricultural soil. The optimal values of parameters of the fractional model developed in this study and Glover-Dumm's model were estimated using the inverse problem method. In the proposed inverse model, a bees algorithm (BA) was used. The results showed that in the homogenous soil, the heterogeneity index was nearly equal to 2 and therefore, the developed mathematical model reduced to the Glover-Dumm's mathematical model. The heterogeneity index of the experimental field soil considered was equal to 1.04; hence, this soil was classified as a very heterogeneous soil. In the experimental field soil, the proposed mathematical model better represented the water table profile between two parallel subsurface drains than the Glover-Dumm's mathematical model. Therefore, it appears that the proposed fractional model presented is a highly general and effective method to estimate the water table profile between two parallel subsurface drains, and the scale effects are robustly reflected by the introduced heterogeneity index. (C) 2013 Elsevier Ltd. All rights reserved.