PubMed İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8650

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Citation - WoS: 0
Citation - Scopus: 0
A 6-point subdivision scheme and its applications for the solution of 2nd order nonlinear singularly perturbed boundary value problems
(Amer inst Mathematical Sciences-aims, 2020) Mustafa, Ghulam; Baleanu, Dumitru; Ejaz, Syeda Tehmina; Anju, Kaweeta; Ahmadian, Ali; Salahshour, Soheil; Ferrara, Massimiliano; 56389; Matematik
In this paper, we first present a 6-point binary interpolating subdivision scheme (BISS) which produces a C-2 continuous curve and 4th order of approximation. Then as an application of the scheme, we develop an iterative algorithm for the solution of 2nd order nonlinear singularly perturbed boundary value problems (NSPBVP). The convergence of an iterative algorithm has also been presented. The 2nd order NSPBVP arising from combustion, chemical reactor theory, nuclear engineering, control theory, elasticity, and fluid mechanics can be solved by an iterative algorithm with 4th order of approximation.
Citation - WoS: 10
Citation - Scopus: 9
A computational study of a stochastic fractal-fractional hepatitis B virus infection incorporating delayed immune reactions via the exponential decay
(Amer inst Mathematical Sciences-aims, 2022) Al Qurashi, Maysaa; Rashid, Saima; Jarad, Fahd; 234808; Matematik
Recently, researchers have become interested in modelling, monitoring, and treatment of hepatitis B virus infection. Understanding the various connections between pathogens, immune systems, and general liver function is crucial. In this study, we propose a higher-order stochastically modified delay differential model for the evolution of hepatitis B virus transmission involving defensive cells. Taking into account environmental stimuli and ambiguities, we presented numerical solutions of the fractal-fractional hepatitis B virus model based on the exponential decay kernel that reviewed the hepatitis B virus immune system involving cytotoxic T lymphocyte immunological mechanisms. Furthermore, qualitative aspects of the system are analyzed such as the existence-uniqueness of the non-negative solution, where the infection endures stochastically as a result of the solution evolving within the predetermined system's equilibrium state. In certain settings, infection-free can be determined, where the illness settles down tremendously with unit probability. To predict the viability of the fractal-fractional derivative outcomes, a novel numerical approach is used, resulting in several remarkable modelling results, including a change in fractional-order delta with constant fractal-dimension pi, delta with changing pi, and delta with changing both delta and pi. White noise concentration has a significant impact on how bacterial infections are treated.
Citation - WoS: 37
Citation - Scopus: 39
A delayed plant disease model with Caputo fractional derivatives
(Springer, 2022) Kumar, Pushpendra; Baleanu, Dumitru; Erturk, Vedat Suat; Inc, Mustafa; Govindaraj, V; 56389; Matematik
We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams-Bashforth-Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study.
Citation - WoS: 152
Citation - Scopus: 184
A fractional differential equation model for the COVID-19 transmission by using the Caputo-Fabrizio derivative
(Springer, 2020) Baleanu, Dumitru; Mohammadi, Hakimeh; Rezapour, Shahram; 56389; Matematik
We present a fractional-order model for the COVID-19 transmission with Caputo-Fabrizio derivative. Using the homotopy analysis transform method (HATM), which combines the method of homotopy analysis and Laplace transform, we solve the problem and give approximate solution in convergent series. We prove the existence of a unique solution and the stability of the iteration approach by using fixed point theory. We also present numerical results to simulate virus transmission and compare the results with those of the Caputo derivative.
Citation - WoS: 36
Citation - Scopus: 36
A hybrid fractional optimal control for a novel Coronavirus (2019-nCov) mathematical model
(Elsevier, 2021) Sweilam, N. H.; AL-Mekhlafi, S. M.; Baleanu, D.; 56389; Matematik
Introduction: Coronavirus COVID-19 pandemic is the defining global health crisis of our time and the greatest challenge we have faced since world war two. To describe this disease mathematically, we noted that COVID-19, due to uncertainties associated to the pandemic, ordinal derivatives and their associated integral operators show deficient. The fractional order differential equations models seem more consistent with this disease than the integer order models. This is due to the fact that fractional derivatives and integrals enable the description of the memory and hereditary properties inherent in various materials and processes. Hence there is a growing need to study and use the fractional order differential equations. Also, optimal control theory is very important topic to control the variables in mathematical models of infectious disease. Moreover, a hybrid fractional operator which may be expressed as a linear combination of the Caputo fractional derivative and the Riemann-Liouville fractional integral is recently introduced. This new operator is more general than the operator of Caputo's fractional derivative. Numerical techniques are very important tool in this area of research because most fractional order problems do not have exact analytic solutions. Objectives: A novel fractional order Coronavirus (2019-nCov) mathematical model with modified parameters will be presented. Optimal control of the suggested model is the main objective of this work. Three control variables are presented in this model to minimize the number of infected populations. Necessary control conditions will be derived. Methods: The numerical methods used to study the fractional optimality system are the weighted average nonstandard finite difference method and the Grunwald-Letnikov nonstandard finite difference method. Results: The proposed model with a new fractional operator is presented. We have successfully applied a kind of Pontryagin's maximum principle and were able to reduce the number of infected people using the proposed numerical methods. The weighted average nonstandard finite difference method with the new operator derivative has the best results than Grunwald-Letnikov nonstandard finite difference method with the same operator. Moreover, the proposed methods with the new operator have the best results than the proposed methods with Caputo operator. Conclusions: The combination of fractional order derivative and optimal control in the Coronavirus (2019-nCov) mathematical model improves the dynamics of the model. The new operator is more general and suitable to study the optimal control of the proposed model than the Caputo operator and could be more useful for the researchers and scientists. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 14
Citation - Scopus: 17
A Mathematical and Statistical Estimation of Potential Transmission and Severity of COVID-19: A Combined Study of Romania and Pakistan
(Hindawi Ltd, 2020) Ozair, Muhammad; Hussain, Takasar; Hussain, Mureed; Awan, Aziz Ullah; Baleanu, Dumitru; Abro, Kashif Ali; 56389; Matematik
During the outbreak of an epidemic, it is of immense interest to monitor the effects of containment measures and forecast of outbreak including epidemic peak. To confront the epidemic, a simple SIR model is used to simulate the number of affected patients of coronavirus disease in Romania and Pakistan. The model captures the growth in case onsets, and the estimated results are almost compatible with the actual reported cases. Through the calibration of parameters, forecast for the appearance of new cases in Romania and Pakistan is reported till the end of this year by analysing the current situation. The constant level of number of patients and time to reach this level is also reported through the simulations. The drastic condition is also discussed which may occur if all the preventive restraints are removed.
Citation - WoS: 27
Citation - Scopus: 29
A mathematical model of the evolution and spread of pathogenic coronaviruses from natural host to human host
(Pergamon-elsevier Science Ltd, 2020) Bozkurt, Fatma; Yousef, Ali; Baleanu, Dumitru; Alzabut, Jehad; 56389; Matematik
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.
Citation - WoS: 10
Citation - Scopus: 15
A novel computational approach to approximate fuzzy interpolation polynomials
(Springer international Publishing Ag, 2016) Jafarian, Ahmad; Jafari, Raheleh; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; 56389; Matematik
This paper build a structure of fuzzy neural network, which is well sufficient to gain a fuzzy interpolation polynomial of the form y(p) = a(n)x(p)(n) +... + a(1)x(p) + a(0) where a(j) is crisp number (for j = 0,..., n), which interpolates the fuzzy data (x(j), y(j)) (for j = 0,..., n). Thus, a gradient descent algorithm is constructed to train the neural network in such a way that the unknown coefficients of fuzzy polynomial are estimated by the neural network. The numeral experimentations portray that the present interpolation methodology is reliable and efficient.
Citation - WoS: 1
Citation - Scopus: 1
A novel fractional model for the projection of households using wealth index quintiles
(Public Library Science, 2022) Ahmad, Shakoor; Javeed, Shumaila; Raza, Saqlain; Baleanu, Dumitru; 56389; Matematik
Forecasting household assets provides a better opportunity to plan their socioeconomic activities for the future. Fractional mathematical models offer to model the asset-holding data into a piece of scientific evidence in addition to forecasting their future value. This research focuses on the development of a new fractional mathematical model based on the wealth index quintile (WIQ) data. To accomplish the objective, we used the system of coupled fractional differential equations by defining the fractional term with the Caputo derivative and verified it with the stability tests considering the steady-state solution. A numerical solution of the model was obtained using the Adams-Bashforth-Moulton method. To validate the model, we used real-time data obtained from the household series of surveys in Punjab, Pakistan. Different case studies that elucidate the effect of quintiles on the population are also presented. The accuracy of results between real-world and simulated data was compared using absolute and relative errors. The synchronization between the simulated results and real-time data verifies the formulation of the fractional WIQ model. This fractional model can be utilized to predict the approximation of the asset-holding of the households. Due to its relative nature, the model also provides the opportunity for the researchers to use the WIQs of their respective regions to forecast the households' socioeconomic conditions.
Citation - WoS: 9
Citation - Scopus: 15
A serious game for improving the decision making skills and knowledge levels of Turkish football referees according to the laws of the game
(Springer international Publishing Ag, 2016) Gulec, Ulas; Yilmaz, Murat; 47439; Bilgisayar Mühendisliği; Yazılım Mühendisliği
Digital game-based learning environments provide emerging opportunities to overcome learning barriers by combining newly developed technologies and traditional game design. This study proposes a quantitative research approach supported by expert validation interviews to designing a game-based learning framework. The goal is to improve the learning experience and decision-making skills of soccer referees in Turkey. A serious game was developed and tested on a group of referees (N = 54). The assessment results of these referees were compared with two sample t-test and the Wilcoxon signed-ranked test for both the experimental group and the control group. The findings of the current study confirmed that a game-based learning environment has greater merit over the paper-based alternatives.
Citation - WoS: 13
Citation - Scopus: 16
A validated active contour method driven by parabolic arc model for detection and segmentation of mitochondria
(Academic Press inc Elsevier Science, 2016) Tasel, Serdar F.; Mumcuoglu, Erkan U.; Hassanpour, Reza Z.; Perkins, Guy; Bilgisayar Mühendisliği; Yazılım Mühendisliği
Recent studies reveal that mitochondria take substantial responsibility in cellular functions that are closely related to aging diseases caused by degeneration of neurons. These studies emphasize that the membrane and crista morphology of a mitochondrion should receive attention in order to investigate the link between mitochondria] function and its physical structure. Electron microscope tomography (EMT) allows analysis of the inner structures of mitochondria by providing highly detailed visual data from large volumes. Computerized segmentation of mitochondria with minimum manual effort is essential to accelerate the study of mitochondrial structure/function relationships. In this work, we improved and extended our previous attempts to detect and segment mitochondria from transmission electron microcopy (TEM) images. A parabolic arc model was utilized to extract membrane structures. Then, curve energy based active contours were employed to obtain roughly outlined candidate mitochondrial regions. Finally, a validation process was applied to obtain the final segmentation data. 3D extension of the algorithm is also presented in this paper. Our method achieved an average F-score performance of 0.84. Average Dice Similarity Coefficient and boundary error were measured as 0.87 and 14 nm respectively. (C) 2016 Elsevier Inc. All rights reserved.
Citation - WoS: 110
Citation - Scopus: 112
Active laser radar systems with stochastic electromagnetic beams in turbulent atmosphere
(Optica Publishing Group, 2008) Cai, Yangjian; Korotkova, Olga; Eyyuboglu, Halil T.; Baykal, Yahya; 7688; 7812
Propagation of stochastic electromagnetic beams through paraxial ABCD optical systems operating through turbulent atmosphere is investigated with the help of the ABCD matrices and the generalized Huygens-Fresnel integral. In particular, the analytic formula is derived for the cross-spectral density matrix of an electromagnetic Gaussian Schell-model (EGSM) beam. We applied our analysis for the ABCD system with a single lens located on the propagation path, representing, in a particular case, the unfolded double-pass propagation scenario of active laser radar. Through a number of numerical examples we investigated the effect of local turbulence strength and lens' parameters on spectral, coherence and polarization properties of the EGSM beam. (C) 2008 Optical Society of America
Citation - WoS: 34
Adaptive fractional-order blood glucose regulator based on high-order sliding mode observer
(inst Engineering Technology-iet, 2019) Delavari, Hadi; Heydarinejad, Hamid; Baleanu, Dumitru; 56389; Matematik
Type I diabetes is described by the destruction of the insulin-producing beta-cells in the pancreas. Hence, exogenous insulin administration is necessary for Type I diabetes patients. In this study, to estimate the states that are not directly available from the Bergman minimal model a high-order sliding mode observer is proposed. Then fractional calculus is combined with sliding mode control (SMC) for blood glucose regulation to create more robustness performance and make more degree of freedom and flexibility for the proposed method. Then an adaptive fractional-order SMC is proposed. The adaptive SMC protect controller against disturbance and uncertainties while the fractional calculus provides robust performance. Numerical simulation verifies that the proposed controllers have better performance in the presence of disturbance and uncertainties without chattering.
Citation - WoS: 7
Citation - Scopus: 16
An analysis on the relationship between safety awareness and safety behaviors of healthcare professionals, Ankara/Turkey
(Oxford Univ Press, 2020) Uzuntarla, Fatma; Kucukali, Serhat; Uzuntarla, Yasin; 20413
Objectives: This descriptive study aims to examine the relationship between the safety awareness of healthcare professional and their safety behaviors. Methods: The study was carried out on 418 healthcare professionals working in a training and research hospital in Ankara/Turkey. The survey method was used as data collection tool. The questionnaire consisted of 3 sections and 18 questions. First section consisted of questions on sociodemographic characteristics and, second section consisted of the awareness scale and third section consisted of safety behaviors scale. Results: The safety awareness and safety behaviors are scored on a scale from 1 (completely disagree) to 5 (completely agree). The safety awareness and safety behaviors has an average score of 3.85 +/- 0.81 and 3.56 +/- 0.82, respectively. The safety awareness and safety behavior levels of healthcare professionals were found to be high. Conclusion: A significant positive correlation was found between safety awareness and safety behaviors and it was concluded that the increase in safety awareness led to an increase in safety behavior.
Citation - WoS: 68
Citation - Scopus: 79
An Efficient Computational Technique for Fractal Vehicular Traffic Flow
(Mdpi, 2018) Kumar, Devendra; Tchier, Fairouz; Singh, Jagdev; Baleanu, Dumitru; 56389; Matematik
In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.
Citation - WoS: 25
Citation - Scopus: 37
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; 56389
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.
Citation - WoS: 18
Citation - Scopus: 24
Analysis for Fractional-Order Predator–Prey Model With Uncertainty
(inst Engineering Technology-iet, 2019) Narayanamoorthy, Samayan; Baleanu, Dumitru; Thangapandi, Kalidas; Perera, Shyam Sanjeewa Nishantha; 56389; Matematik
Here, the authors analyse the fractional-order predator-prey model with uncertainty, due to the vast applications in various ecological systems. The most of the ecological model do not have exact analytic solution, so they proposed a numerical technique for an approximate solution. In the proposed method, they have implemented the higher order term into the fractional Euler method to enhance the precise solution. Further, the present attempt is aimed to discuss the solutions of the FPPM with uncertainty (fuzzy) initial conditions. The initial conditions of the predator-prey model were taken as fuzzy initial conditions due to the fact that the ecological model highly depends on uncertain parameters such as growth/decay rate, climatic conditions, and chemical reactions. Finally, the numerical example manifest that the proposed method is authentic, applicable, easy to use from a computational viewpoint and the acquired outcomes are balanced with the existing method (HPM), which shows the efficiency of the proposed method.
Citation - WoS: 12
Analysis of Dengue Transmission Dynamic Model by Stability and Hopf Bifurcation with Two-Time Delays
(Imr Press, 2023) Murugadoss, Prakash Raj; Ambalarajan, Venkatesh; Sivakumar, Vinoth; Dhandapani, Prasantha Bharathi; Baleanu, Dumitru; 56389; Matematik
Background: Mathematical models reflecting the epidemiological dynamics of dengue infection have been discovered dating back to 1970. The four serotypes (DENV-1 to DENV-4) that cause dengue fever are antigenically related but different viruses that are transmitted by mosquitoes. It is a significant global public health issue since 2.5 billion individuals are at risk of contracting the virus. Methods: The purpose of this study is to carefully examine the transmission of dengue with a time delay. A dengue transmission dynamic model with two delays, the standard incidence, loss of immunity, recovery from infectiousness, and partial protection of the human population was developed. Results: Both endemic equilibrium and illness-free equilibrium were examined in terms of the stability theory of delay differential equations. As long as the basic reproduction number (R0) is less than unity, the illness-free equilibrium is locally asymptotically stable; however, when R0 exceeds unity, the equilibrium becomes unstable. The existence of Hopf bifurcation with delay as a bifurcation parameter and the conditions for endemic equilibrium stability were examined. To validate the theoretical results, numerical simulations were done. Conclusions: The length of the time delay in the dengue transmission epidemic model has no effect on the stability of the illness-free equilibrium. Regardless, Hopf bifurcation may occur depending on how much the delay impacts the stability of the underlying equilibrium. This mathematical modelling is effective for providing qualitative evaluations for the recovery of a huge population of afflicted community members with a time delay.
Citation - WoS: 64
Citation - Scopus: 83
Analysis of fractional model of guava for biological pest control with memory effect
(Elsevier, 2021) Singh, Jagdev; Ganbari, Behzad; Kumar, Devendra; Baleanu, Dumitru; 56389; Matematik
Introduction: Fractional operators find their applications in several scientific and engineering processes. We consider a fractional guava fruit model involving a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. The fractional guava fruit model is considered as a Lotka-Volterra nature. Objectives: The main objective of this work is to study a guava fruit model associated with a non-local additionally non-singular fractional derivative for the interaction into guava pests and natural enemies. Methods: Existence and uniqueness analysis of the solution is evaluated effectively by using Picard Lindelof approach. An approximate numerical solution of the fractional guava fruit problem is obtained via a numerical scheme. Results: The positivity analysis and equilibrium analysis for the fractional guava fruit model is discussed. The numerical results are demonstrated to prove our theoretical results. The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters is discussed. Conclusion: The graphical behavior of solution of the fractional guava problem at the distinct fractional order values and at various parameters shows new vista and interesting phenomena of the model. The results are indicating that the fractional approach with non-singular kernel plays an important role in the study of different scientific problems. The suggested numerical scheme is very efficient for solving nonlinear fractional models of physical importance. (C) 2021 The Authors. Published by Elsevier B.V. on behalf of Cairo University.
Citation - WoS: 183
Citation - Scopus: 193
Analysis of reciprocity of cos-Gaussian and cosh-Gaussian laser beams in a turbulent atmosphere
(Optical Soc Amer, 2004) Eyyuboglu, HT; Baykal, Y; 7688; 7812
In a turbulent atmosphere, starting with a cos-Gaussian excitation at the source plane, the average intensity profile at the receiver plane is formulated. This average intensity profile is evaluated against the variations of link lengths, turbulence levels, two frequently used free-space optics wavelengths, and beam displacement parameters. We show that a cos-Gaussian beam, following a natural diffraction, is eventually transformed into a cosh-Gaussian beam. Combining our earlier results with the current findings, we conclude that cos-Gaussian and cosh-Gaussian beams act in a reciprocal manner after propagation in turbulence. The rates (paces) of conversion in the two directions are not the same. Although the conversion of cos-Gaussian beams to cosh-Gaussian beams can happen over a wide range of turbulence levels (low to moderate to high), the conversion of cosh-Gaussian beams to cos-Gaussian beams is pronounced under relatively stronger turbulence conditions. Source and propagation parameters that affect this reciprocity have been analyzed. (C) 2004 Optical Society of America.

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