Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 2Citation - Scopus: 2Computational Algorithms for the Analysis of Cancer Virotherapy Model(Tech Science Press, 2022) Baleanu, Dumitru; Rafiq, Muhammad; Abbas, Syed Zaheer; Siddique, Abubakar; Javed, Umer; Nazir, Zaighum; Raza, AliCancer is a common term for many diseases that can affect any part of the body. In 2020, ten million people will die due to cancer. A worldwide leading cause of death is cancer by the World Health Organization (WHO) report. Interaction of cancer cells, viral therapy, and immune response are identified in this model. Mathematical and computational modeling is an effective tool to predict the dynamics of cancer virotherapy. The cell population is categorized into three parts like uninfected cells (x), infected cells (y), virus-free cells (v), and immune cells (z). The modeling of cancer-like diseases is based on the law of mass action (the rate of change of reacting substances is directly proportional to the product of interacting substances). Positivity, boundedness, equilibria, threshold analysis, are part of deterministic modeling. Later on, a numerical analysis is designed by using the standard and non-standard finite difference methods. The non-standard finite difference method is developed to study the long-term behavior of the cancer model. For its efficiency, a comparison of the methods is investigated.Article Bio-Inspired Modelling of Disease Through Delayed Strategies(Tech Science Press, 2022) Baleanu, Dumitru; Raza, Ali; Anwar, Pervez; Ahmed, Nauman; Rafiq, Muhammad; Cheema, Tahir Nawaz; Nasir, AroojIn 2020, the reported cases were 0.12 million in the six regions to the official report of the World Health Organization (WHO). For most children infected with leprosy, 0.008629 million cases were detected under fifteen. The total infected ratio of the children population is approximately 4.4 million. Due to the COVID-19 pandemic, the awareness programs implementation has been disturbed. Leprosy disease still has a threat and puts people in danger. Nonlinear delayed modeling is critical in various allied sciences, including computational biology, computational chemistry, computational physics, and computational economics, to name a few. The time delay effect in treating leprosy delayed epidemic model is investigated. The whole population is divided into four groups: those who are susceptible, those who have been exposed, those who have been infected, and those who have been vaccinated. The local and global stability of well-known conclusions like the Routh Hurwitz criterion and the Lyapunov function has been proven. The parameters' sensitivity is also examined. The analytical analysis is supported by computer results that are presented in a variety of ways. The proposed approach in this paper preserves equilibrium points and their stabilities, the existence and uniqueness of solutions, and the computational ease of implementation.Article Citation - WoS: 1Citation - Scopus: 4Fractional Modeling of Cancer With Mixed Therapies(Imr Press, 2023) Ul Abdeen, Zain; Baleanu, Dumitru; Javeed, ShumailaBackground: Cancer is the biggest cause of mortality globally, with approximately 10 million fatalities expected by 2020, or about one in every six deaths. Breast, lung, colon, rectum, and prostate cancers are the most prevalent types of cancer. Methods: In this work, fractional modeling is presented which describes the dynamics of cancer treatment with mixed therapies (immunotherapy and chemotherapy). Mathematical models of cancer treatment are important to understand the dynamical behavior of the disease. Fractional models are studied considering immunotherapy and chemotherapy to control cancer growth at the level of cell populations. The models consist of the system of fractional differential equations (FDEs). Fractional term is defined by Caputo fractional derivative. The models are solved numerically by using Adams-Bashforth-Moulton method. Results: For all fractional models the reasonable range of fractional order is between beta = 0.6 and beta = 0.9. The equilibrium points and stability analysis are presented. Moreover, positivity and boundedness of the solution are proved. Furthermore, a graphical representation of cancerous cells, immunotherapy and chemotherapy is presented to understand the behaviour of cancer treatment. Conclusions: At the end, a curve fitting procedure is presented which may help medical practitioners to treat cancer patients.Article Citation - WoS: 6Citation - Scopus: 7Treatment of Polio Delayed Epidemic Model Via Computer Simulations(Tech Science Press, 2022) Baleanu, Dumitru; Raza, Ali; Rafiq, Muhammad; Soori, Atif Hassan; Naveed, MuhammadThrough the study, the nonlinear delayed modelling has vital significance in the different field of allied sciences like computational biology, computational chemistry, computational physics, computational economics and many more. Polio is a contagious viral illness that in its most severe form causes nerve injury leading to paralysis, difficulty breathing and sometimes death. In recent years, developing regions like Asia, Africa and sub-continents facing a dreadful situation of poliovirus. That is the reason we focus on the treatment of the polio epidemic model with different delay strategies in this article. Polio delayed epidemic model is categorized into four compartments like susceptible, exposed, infective and vaccinated classes. The equilibria, positivity, boundedness, and reproduction number are investigated. Also, the sensitivity of the parameters is analyzed. Well, known results like the Routh Hurwitz criterion and Lyapunov function stabilities are investigated for polio delayed epidemic model in the sense of local and global respectively. Furthermore, the computer simulations are presented with different traditions in the support of the analytical analysis of the polio delayed epidemic model.Article Citation - WoS: 18Citation - Scopus: 24Rotating 3d Flow of Hybrid Nanofluid on Exponentially Shrinking Sheet: Symmetrical Solution and Duality(Mdpi, 2020) Omar, Zurni; Dero, Sumera; Baleanu, Dumitru; Khan, Ilyas; Lund, Liaquat AliThis article aims to study numerically the rotating, steady, and three-dimensional (3D) flow of a hybrid nanofluid over an exponentially shrinking sheet with the suction effect. We considered water as base fluid and alumina (Al2O3), and copper (Cu) as solid nanoparticles. The system of governing partial differential equations (PDEs) was transformed by an exponential similarity variable into the equivalent system of ordinary differential equations (ODEs). By applying a three-stage Labatto III-A method that is available in bvp4c solver in the Matlab software, the resultant system of ODEs was solved numerically. In the case of the hybrid nanofluid, the heat transfer rate improves relative to the viscous fluid and regular nanofluid. Two branches were obtained in certain ranges of the involved parameters. The results of the stability analysis revealed that the upper branch is stable. Moreover, the results also indicated that the equations of the hybrid nanofluid have a symmetrical solution for different values of the rotation parameter (Omega).Article Citation - WoS: 21Citation - Scopus: 26Robust Stabilization of Fractional-Order Chaotic Systems With Linear Controllers: Lmi-Based Sufficient Conditions(Sage Publications Ltd, 2014) Kuntanapreeda, Suwat; Delavari, Hadi; Baleanu, Dumitru; Faieghi, Mohammad RezaThis paper is concerned with the problem of robust state feedback controller design to suppress fractional-order chaotic systems. A general class of fractional-order chaotic systems is considered and it is assumed that the systems' equations depend on bounded uncertain parameters. We transform the chaotic system equations into linear interval systems, and a sufficient stabilizability condition is derived in terms of linear matrix inequality (LMI). Then, an appropriate feedback gain is introduced to bring the chaotic states to the origin. Such design will result in a simple but effective controller. Several numerical simulations have been carried out to verify the effectiveness of the theoretic results.Article Citation - WoS: 22Citation - Scopus: 25Optimal Control Model for the Transmission of Novel Covid-19(Tech Science Press, 2021) Nasidi, Bashir Ahmad; Baleanu, Dumitru; Baba, Isa AbdullahiAs the corona virus (COVID-19) pandemic ravages socio-economic activities in addition to devastating infectious and fatal consequences, optimal control strategy is an effective measure that neutralizes the scourge to its lowest ebb. In this paper, we present a mathematical model for the dynamics of COVID-19, and then we added an optimal control function to the model in order to effectively control the outbreak. We incorporate three main control efforts (isolation, quarantine and hospitalization) into the model aimed at controlling the spread of the pandemic. These efforts are further subdivided into five functions; u(1)(t) (isolation of the susceptible communities), u(2)(t) (contact track measure by which susceptible individuals with contact history are quarantined), u(3)(t) (contact track measure by which infected individualsare quarantined), u(4)(t) (control effort of hospitalizing the infected I-1) and u(5)(t) (control effort of hospitalizing the infected I-2). We establish the existence of the optimal control and also its characterization by applying Pontryaging maximum principle. The disease free equilibrium solution (DFE) is found to be locally asymptotically stable and subsequently we used it to obtain the key parameter; basic reproduction number. We constructed Lyapunov function to which global stability of the solutions is established. Numerical simulations show how adopting the available control measures optimally, will drastically reduce the infectious populations.Article Citation - WoS: 13Citation - Scopus: 13Numerical Solution of Highly Non-Linear Fractional Order Reaction Advection Diffusion Equation Using the Cubic B-Spline Collocation Method(Walter de Gruyter Gmbh, 2022) Das, Subir; Rajeev; Baleanu, Dumitru; Dwivedi, Kushal DharIn this article, the approximate solution of the fractional-order reaction advection-diffusion equation with the prescribed initial and boundary conditions is found with the help of a cubic B-spline collocation method, which is unconditionally stable and convergent. The accuracy of the scheme is validated by applying the method on four existing problems having analytical solutions and through the evaluation of the absolute errors between numerical results and the exact solutions for different particular cases. Applying the proposed method on the last two numerical problems, it is shown that the method performs better than the existing methods even for very less number of spatial and temporal discretizations. The main contribution of the article is to develop an efficient method to solve the proposed fractional order nonlinear problem and to find the effect on solute concentration graphically due to increase in the non-linearity in the diffusion term for different particular values of parameters.Article Citation - WoS: 29Citation - Scopus: 35Magnetized Flow of Cu + Al2o3 + H2o Hybrid Nanofluid in Porous Medium: Analysis of Duality and Stability(Mdpi, 2020) Omar, Zurni; Dero, Sumera; Khan, Ilyas; Baleanu, Dumitru; Nisar, Kottakkaran Sooppy; Lund, Liaquat AliIn this analysis, we aim to examine the heat transfer and flow characteristics of a copper-aluminum/water hybrid nanofluid in the presence of viscous dissipation, magnetohydrodynamic (MHD), and porous medium effect over the shrinking sheet. The governing equations of the fluid model have been acquired by employment of the model of Tiwari and Das, with additional properties of the hybrid nanofluid. The system of partial differential equations (PDEs) has been converted into ordinary differential equations (ODEs) by adopting the exponential similarity transformation. Similarity transformation is an essential class of phenomenon where the symmetry of the scale helps to reduce the number of independent variables. Note that ODE solutions demonstrate the PDEs symmetrical behavior for the velocity and temperature profiles. With BVP4C solver in the MATLAB program, the system of resulting equations has been solved. We have compared the present results with the published results and found in excellent agreements. The findings of the analysis are also displayed and discussed in depth graphically and numerically. It is discovered that two solutions occur in definite ranges of suction and magnetic parameters. Dual (no) similarity solutions can be found in the range of S-c <= S and M-c <= M (S-c > S and M-c > M). By performing stability analysis, the smallest values of eigenvalue are obtained, suggesting that a stable solution is the first one. Furthermore, the graph of the smallest eigenvalue shows symmetrical behavior. By enhancing the Eckert number values the temperature of the fluid is raised.Article Citation - WoS: 29Citation - Scopus: 33Dynamical Transmission of Coronavirus Model With Analysis and Simulation(Tech Science Press, 2021) Baleanu, Dumitru; Akgul, Ali; Ahmad, Aqeel; Saleem, Muhammad Umer; Farman, MuhammadCOVID-19 acts as a serious challenge to the whole world. Epidemiological data of COVID-19 is collected through media and web sources to analyze and investigate a system of nonlinear ordinary differential equation to understand the outbreaks of this epidemic disease. We analyze the diseases free and endemic equilibrium point including stability of the model. The certain threshold value of the basic reproduction number R-0 is found to observe whether population is in disease free state or endemic state. Moreover, the epidemic peak has been obtained and we expect a considerable number of cases. Finally, some numerical results are presented which show the effect of parameters estimation and different step size on our obtained solutions at the real data of some countries to check the actual behavior of the COVID-19 at different countries.