Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 99Citation - Scopus: 113Recent Developments of Energy Management Strategies in Microgrids: an Updated and Comprehensive Review and Classification(Pergamon-elsevier Science Ltd, 2023) Baleanu, Dumitru; Abbasi, Ali RezaEnergy is one of the essential foundations for the sustainable development of human society, so its management is necessary. Energy management system (EMS) can be explained as the procedure of optimizing, planning, controlling, monitoring, and saving energy to maximize operations and efficiency and minimize consumption. Microgrid (MG) requires EMS as an efficient and optimal tool owing to the stochastic nature of electrical loads and renewable sources. Moreover, energy management system is responsible for operation of a MG in reliable, secure and economical manner in either states of grid-connected or disconnected. Many literatures have recently focused on the expansion of advanced strategies of the MG energy management for establishing a self-sustained MG in both industrial and academic research. Thus, a comparative research is needed for having a 360 degrees viewpoint of the energy management domain in MGs. In this regard, this research investigates a comparative and critical analysis of the developed strategies of the energy management for the MGs from different views and aspects from 2009 to 2022. The review strategy systematically adopted by the author includes: (i) Extracting research papers relevant to energy management in MGs; (ii) Filtering the significant papers to prepare a database of related research papers (iii) Classifying the used methods for EMS based on the technique, control strategies, and structure; (iv) Discussing potential directions for future studies. In a wider outlook, this research provides a systematic and updated review of energy management strategies for MGs developed by different researchers. The author hopes that academicians and practitioners can use the suggested framework as well as the offers presented for further studies on this significant yet sophisticated issue.Article Citation - WoS: 103Citation - Scopus: 107Some Novel Mathematical Analysis on the Fractal-Fractional Model of the Ah1n1/09 Virus and Its Generalized Caputo-Type Version(Pergamon-elsevier Science Ltd, 2022) Avci, Ibrahim; Kumar, Pushpendra; Baleanu, Dumitru; Rezapour, Shahram; Etemad, SinaIn this paper, we formulate a new model of a particular type of influenza virus called AH1N1/09 in the framework of the four classes consisting of susceptible, exposed, infectious and recovered people. For the first time, we here investigate this model with the help of the advanced operators entitled the fractal-fractional operators with two fractal and fractional orders via the power law type kernels. The existence of solution for the mentioned fractal-fractional model of AH1N1/09 is studied by some special mappings such as ?-psi-contractions and ?-admissibles. The Leray-Schauder theorem is also applied for this aim. After investigating the stability criteria in four versions, to approximate the desired numerical solutions, we implement Adams-Bashforth (AB) scheme and simulate the graphs for different data on the fractal and fractional orders. Lastly, we convert our fractal-fractional AH1N1/09 model into a fractional model via the generalized Liouville-Caputo-type (GLC-type) operators and then, we simulate new graphs caused by the new numerical scheme called Kumar-Erturk method.Editorial Citation - WoS: 1Citation - Scopus: 2Editorial: Recent Advances in Computational Biology(Pergamon-elsevier Science Ltd, 2022) Srivastava, Hari Mohan; Cattani, Carlo; Baleanu, DumitruArticle Citation - WoS: 4Citation - Scopus: 5Swarming Optimization To Analyze the Fractional Derivatives and Perturbation Factors for the Novel Singular Model(Pergamon-elsevier Science Ltd, 2022) Ben Said, Salem; Baleanu, Dumitru; Sabir, Zulqurnain; Said, Salem BenThe aim of this research is to present an investigation based on the fractional derivatives and perturbation factors for the novel singular system. This study also presents a novel design of the fractional perturbed singular system by using the conventional Lane-Emden form together with the features of fractional order values, singular points, perturbed terms and shape factors. An analysis based on the fractional order derivative and perturbation factors is provided using the novel singular form of the Lane-Emden system in two different ways with three different variations. The numerical representations based on the novel design of the fractional perturbed singular system are presented through the Meyer wavelet neural networks (MWNNs). The optimization is performed by using the hybrid efficiency of the global swarming particle swarm optimization (PSO) scheme along with the local interior -point algorithm (IPA). The modeling through the MWNN is signified through the novel fractional perturbed singular system through the mean square error along with the PSOIPA optimization. The exactness, verification, endorsement and excellence of the novel fractional perturbed singular system are authenticated through the comparison of the obtained and the true solutions. The reliability of the stochastic procedure is performed by using the statistical measures with a large domain of the dataset to analyze the fractional derivatives and perturbation factors for the novel singular system.Article Citation - WoS: 30Citation - Scopus: 37Effect of Laser Welding Parameters on the Temperature Distribution, Microstructure and Mechanical Properties of Dissimilar Weld Joint of Inconel 625 and Stainless Steel 304(Pergamon-elsevier Science Ltd, 2022) Jam, Jafar Eskandari; Beni, Mohsen Heydari; Kholoud, Mohammad Javad; Baleanu, Dumitru; Shahraki, Majid Eskandari; Ghaemi, Ferial; Yan, LiLaser welding technology and investigation of temperature distribution can serve as an important criterion for performing high-quality joints. In this experimental study, dissimilar laser welding is performed between stainless steel 304 (S.S 304) and Inconel 625 alloys. The temperature is measured by changing such parameters of laser as laser power, welding speed and nozzle distance. The parameters variations are 300-400 W, 240-480 mm/min and 0-4 mm for the laser power, welding speed and nozzle distance, respectively. Examining the parameters shows that the change in the laser power due to temperature changes had a greater effect on temperature changes around the Inconel 625 side melt pool; also, the rate of change was about twice that of S.S 304. In the case of the S.S 304 alloy, the temperature increase was occurred at a slower rate and the evaporation rate of the material on the S.S304 side is higher than that of Inconel 625 superalloy. As a result, the rate of temperature increase is slower and part of the laser energy is used to evaporate S.S 304. The microstructural changes in the boundary of the fusion zone with the base metal Inconel 625 are clearly visible.Article Citation - WoS: 28Citation - Scopus: 30Dynamics of Hiv-Tb Coinfection Model Using Classical and Caputo Piecewise Operator: a Dynamic Approach With Real Data From South-East Asia, European and American Regions(Pergamon-elsevier Science Ltd, 2022) Liu, Zixin; Pang, Yicheng; Akgul, Ali; Baleanu, Dumitru; Xu, ChangjinIn this study, we analyse the behaviour of the coinfection of the HIV-TB model using a piecewise operator in the classical-Caputo sense. For the aforementioned disease model, we present the existence as well as the uniqueness of a solution having a piecewise derivative. We also study the different versions of stability using Ulam-Hyers stability in nonlinear analysis. We use the piecewise Newton polynomial technique to obtain an approximation of the solution to the proposed problem. The simulations for the suggested coinfection model are presented. The simulations are carried out for the disease-free as well as endemic equilibrium. Additionally, the comparison between the simulated and real data is presented, where we obtain the best-fitted dynamics of the infected class with TB.Article Citation - WoS: 16Citation - Scopus: 20Different Strategies To Confront Maize Streak Disease Based on Fractional Optimal Control Formulation(Pergamon-elsevier Science Ltd, 2022) Baleanu, Dumitru; Ali, Hegagi Mohamed; Ameen, Ismail GadIn this paper, we propose a general formulation for the transmission dynamics of maize streak virus (MSV) pathogen interaction with a pest invasion in the maize plant. The mathematical formalism for this model is dependent on Caputo fractional operator with modification of its parameters. In the considered model, the total population of maize plants is divided into two classes: susceptible, infected maize and the total population of leafhopper vector contains two compartments: susceptible, infected leafhopper vector, with a compartment for MSV pathogen. In addition, this fractional-order model (FOM) is involving the proportion of three controls u1, u2 and u3 which namely respectively prevention, quarantine and chemical control. We present the positivity and boundedness of the projected solutions to assure the feasibility of solutions of this FOM. The control reproduction number (Rc) is derived by next generation matrix (NGM) method and showed graphically the effect of the controls for each proposed strategy on the behavior of Rc. The local stability analysis for all possible equilibrium points (EPs) has been examined in detail. Moreover, the fractional optimal control problem (FOCP) is characterized and fractional necessary optimality conditions (NOCs) are derived by using Pontryagin's maximum principle (PMP). These NOCs are solved numerically, where the state and co -state equations based on the left Caputo fractional derivative (CFD). We offer four strategies to illustrate the effects of the proposed controls to investigate the preferable strategy for the elimination of maize streak disease (MSD), as each one of these strategies is able to alleviate this disease at a specific time. Finally, simulations are performed utilizing MATLAB with realistic ecological parameter values to demonstrate the obtained theoretical results. Comparative studies illustrated that infection of maize plants can be reduced through the proposed model, which has a significant impact on plant epidemiology.Article Citation - WoS: 111Citation - Scopus: 123Stability Analysis and System Properties of Nipah Virus Transmission: a Fractional Calculus Case Study(Pergamon-elsevier Science Ltd, 2023) Shekari, Parisa; Torkzadeh, Leila; Ranjbar, Hassan; Jajarmi, Amin; Nouri, Kazem; Baleanu, DumitruIn this paper, we establish a Caputo-type fractional model to study the Nipah virus transmission dynamics. The model describes the impact of unsafe contact with an infectious corpse as a possible way to transmit this virus. The corresponding area to the system properties, including the positivity and boundedness of the solution, is explored by using the generalized fractional mean value theorem. Also, we investigate sufficient conditions for the local and global stability of the disease-free and the endemic steady-states based on the basic reproduction number R0. To show these important stability features, we employ fractional Routh-Hurwitz criterion and LaSalle's invariability principle. For the implementation of this epidemic model, we also use the Adams-Bashforth-Moulton numerical method in a fractional sense. Finally, in addition to compare the fractional and classical results, as one of the main goals of this research, we demonstrate the usefulness of minimal unsafe touch with the infectious corpse. Simulation and comparative results verify the theoretical discussions.Article Citation - WoS: 10Citation - Scopus: 11The Impact of Standard and Nonstandard Finite Difference Schemes on Hiv Nonlinear Dynamical Model(Pergamon-elsevier Science Ltd, 2023) Bukhsh, Imam; Khan, Ihsan Ullah; Asjad, Muhammad Imran; Eldin, Sayed M.; Abd El-Rahman, Magda; Baleanu, Dumitru; Li, Shuo; El-Rahman, Magda AbdMathematical models are enormously valuable in recognition the characteristics of infectious afflictions. The present study describes and analyses a nonlinear Susceptible-Infected (S center dot I) type mathematical model for HIV/ AIDS. To better comprehend the dynamics of disease diffusion, it is assumed that by giving AIDS patients timely Anti Retroviral Therapy (ART), their transition into HIV infected class is attainable. The ART treatment can reduce or manage the spread of disease among individuals that can extend their life for some more years. For the model, the basic reproduction number is formed which provides a base to study the stability of disease free and endemic equilibria. To understand the entire dynamical behavior of the model, standard finite difference (SFD) schemes such as Runge-Kutta of order four (RK-4) and forward Euler schemes and nonstandard finite difference (NSFD) scheme are implemented. The goal of constructing the NSFD scheme for differential equations is to ensure that it is dynamically reliable, while maintaining important dynamical properties like the positivity of the solutions and its convergence to equilibria of continuous model for all finite step sizes. However, the essential characteristics of the continuous model cannot be properly maintained by the Euler and RK-4 schemes, leading to the possibility of numerical solutions that are not entirely similar to those of the original model. For the NSFD scheme, the Routh-Hurwitz criterion is used to assess the local stability of disease-free and endemic equilibria. To explain the global stability of both the equilibria, Lyapunov functions are offered. To verify the theoretical findings and validate the dynamical aspects of the abovementioned schemes, numerical simulations are also provided. The outcomes offered in this study may be engaged as an effective tool for forecasting the progression of HIV/AIDS epidemic diseases.Article Citation - WoS: 38Citation - Scopus: 45Novel Dynamics of the Zoomeron Model Via Different Analytical Methods(Pergamon-elsevier Science Ltd, 2023) Baleanu, Dumitru; Ali, M. Zulfikar; Harun-Or-Roshid; Ullah, Mohammad SafiWe apply the novel Kudryashov scheme, the G1 & PRIME; approach, and the G & PRIME; G & PRIME;+G+A technique to handle the Zoomeron model for the first time, which yields several kinds of soliton solutions with some novel dynamic properties. The proposed model handles specific incidents of soliton structures with distinctive characteristics that arise in laser sciences, fluid mechanics, and nonlinear optics. We observe dark soliton, bright soliton, periodic waves, kink waves, anti-kink waves, and breather waves for the mentioned equation by symbolic calculation. The suggested model also produces lump-type breather waves. Density, 3D, and 2D images are used to exhibit the dynamics of the adopted outcomes. The results will be crucial for future research on higher-order nonlinear models.