WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Commutativity of Cascaded Connected Fractional Order Linear Time-Varying Systems(World Scientific Publ Co Pte Ltd, 2025) Ibrahim, Salisu; Isah, Abdulnasir; Iqbal, Mujahid; Chang, Phang; Baleanu, DumitruIn this work, we present a comprehensive study of the commutativity of fractional-order linear time-varying systems (LTVSs). Commutativity is a fundamental property in the analysis and control of dynamic systems and is often used to simplify the design of controllers. Fractional-order systems, which are characterized by a noninteger-order derivative, have been widely studied in recent years due to their ability to model a wide range of phenomena. However, the commutativity of fractional-order LTVSs has not been widely explored. In this work, we present a comprehensive study of the commutativity of fractional-order LTVSs. We first provide a mathematical definition of commutativity for these systems and demonstrate that it is equivalent to the commutativity of their transfer functions. We then propose a method for verifying the general condition for commutativity of fractional-order LTVSs under zero initial conditions (ICs) and prove it mathematically. Based on our findings, we realized that the commutative requirements, properties, theories, and conditions are general for fractional-order LTVSs, please observed that some fractional-order LTVSs are commutative, some are not commutative, while some are commutative under certain conditions. Based on this fact, we can say that not all fractional-order LTVSs are commutative.We apply explicit commutative results to several examples of fractional-order LTVSs. Our theoretical and simulation results show a good agreement and prove that our fractional-order LTVSs are commutative under certain conditions, moreover, the commutativity property holds for certain conditions and classes of fractional-order LTVSs, but not for others. Because of the application of fraction commutativity in various fields of science and engineering, we find it necessary to come up with explicit results for the first time.Editorial Citation - WoS: 1Citation - Scopus: 1Editorial Special Issue Section on Fractal Ai-Based Analyses and Applications To Complex Systems: Part Ii(World Scientific Publ Co Pte Ltd, 2022) Karaca, Yeliz; Baleanu, Dumitru; Moonis, Majaz; Muhammad, Khan; Zhang, Yu-Dong; Gervasi, OsvaldoArticle Citation - WoS: 11Citation - Scopus: 12Some Symmetric Properties and Applications of Weighted Fractional Integral Operator(World Scientific Publ Co Pte Ltd, 2023) Samraiz, Muhammad; Mehmood, Ahsan; Jarad, Fahd; Naheed, Saima; Wu, ShanheIn this paper, a weighted generalized fractional integral operator based on the Mittag-Leffler function is established, and it exhibits symmetric characteristics concerning classical operators. We demonstrate the semigroup property as well as the boundedness of the operator in absolute continuous like spaces. In this work, some applications with graphical representation are also considered. Finally, we modify the weighted generalized Laplace transform and then applied it to the newly defined weighted fractional integral operator. The defined operator is an extension and generalization of classical Riemann-Liouville and Prabhakar integral operators.Article Citation - WoS: 2Citation - Scopus: 2Numerical Analysis for Hidden Chaotic Behavior of a Coupled Memristive Dynamical System Via Fractal-Fractional Operator Based on Newton Polynomial Interpolation(World Scientific Publ Co Pte Ltd, 2023) Ahmad, Shabir; Yassen, Mansour F.; Asiri, Saeed Ahmed; Ashraf, Abdelbacki M. M.; Saifullah, Sayed; Jarad, Fahd; Abdelmohsen, Shaimaa A. M.Dynamical features of a coupled memristive chaotic system have been studied using a fractal-fractional derivative in the sense of Atangana-Baleanu. Dissipation, Poincare section, phase portraits, and time-series behaviors are all examined. The dissipation property shows that the suggested system is dissipative as long as the parameter g > 0. Similarly, from the Poincare section it is observed that, lowering the value of the fractal dimension, an asymmetric attractor emerges in the system. In addition, fixed point notions are used to analyze the existence and uniqueness of the solution from a fractal-fractional perspective. Numerical analysis using the Adams-Bashforth method which is based on Newton's Polynomial Interpolation is performed. Furthermore, multiple projections of the system with different fractional orders and fractal dimensions are quantitatively demonstrated, revealing new characteristics in the proposed model. The coupled memristive system exhibits certain novel, strange attractors and behaviors that are not observable by the local operators.Article Citation - WoS: 2Citation - Scopus: 5Comparative Performance Analysis of Filtering Methods for Removing Baseline Wander Noise From an Ecg Signal(World Scientific Publ Co Pte Ltd, 2024) Ozaydin, Selma; Ahmad, ImteyazECG signals play a vital role in the diagnosis of cardiovascular conditions. However, they often suffer from the effects of various noise sources, including baseline wandering, respiratory artifact noise, power line interference and electrode motion artifacts. To overcome these challenges, it is imperative to implement low-frequency signal noise reduction strategies. Such strategies aim to significantly improve the quality of ECG signals, thus promoting more accurate and reliable diagnosis of cardiovascular disorders. This paper conducts a comparative analysis to assess the effectiveness of commonly used filtering and wavelet techniques in reducing Baseline Wander (BW) noise within ECG signals generated by the influence of breathing or electrode movements. It is common to observe the selection and evaluation of only one particular technique in the existing literature. In contrast, this study aims to provide a comprehensive comparative analysis, providing insight into the performance and relative merits of different techniques. Our research uses both filtering and Discrete Wavelet Transform (DWT) techniques in baseline noise removal. In this context, a reference point is established utilizing noise-free signals and a meticulous investigation of the wavelet-based approach that most effectively eliminates the resulting noise is provided. Subsequently, we assess the reference input and output signal via Signal-to-Noise Ratio (SNR) and Kolmogorov-Smirnov statistical test measurements. The most important contribution of this work to the scientific community resides in the comprehensive examination of IIR/FIR-based and wavelet method-based filtering methods capable of yielding the highest SNR levels across various ECG signals with various types of BW noise. Additionally, the effectiveness of the Chebychev-II filter in BW noise removal is highlighted. Our study was conducted using the MATLAB platform and code command lines were shared to facilitate the reproduction of our study by other researchers. It is considered that this study will be an important reference in the selection of effective techniques for removing BW noise within ECG signals.Article Citation - WoS: 8Citation - Scopus: 10Analytical Treatments To Systems of Fractional Differential Equations With Modified Atangana-Baleanu Derivative(World Scientific Publ Co Pte Ltd, 2023) Syam, Muhammed I.; Baleanu, Dumitru; Al-Refai, MohammedThe solutions of systems of fractional differential equations depend on the type of the fractional derivative used in the system. In this paper, we present in closed forms the solutions of linear systems involving the modified Atangana-Baleanu derivative that has been introduced recently. For the nonlinear systems, we implement a numerical scheme based on the collocation method to obtain approximate solutions. The applicability of the results is tested through several examples. We emphasize here that certain systems with the Atangana-Baleanu derivative admit no solutions which is not the case with the modified derivative.Article Citation - WoS: 2Citation - Scopus: 9Predicting Financial Failure of the Turkish Banks(World Scientific Publ Co Pte Ltd, 2006) Doganay, M. Mete; Ceylan, Nildag Basak; Aktas, Ramazan; Akta, RamazanBanks are the most important financial institutions in Turkey because other financial institutions are not developed efficiently yet. Turkish banks experienced financial difficulties and a substantial amount of banks failed in the past. This event urged the government to initiate measures to prevent banks from getting into financial difficulties. As a result of these measures, Turkish banking system currently seems to be very attractive for the foreign investors willing to invest in this sector. One of the main concerns of the foreign investors is a possibility of a new banking crisis although it is very remote at this time. The purpose of this study is to develop early warning systems predicting the financial failure at least three years ahead of financial date. A number of multivariate statistical models such as multiple regression, discriminant analysis, logit, probit are used. We found that the most appropriate model is logit. The significant variables obtained from the models explain very well the causes of the bank failures. Our models can be used to assist interested parties to predict the probability of financial failure of Turkish banks.Article Citation - WoS: 3Citation - Scopus: 3On Ritz Approximation for a Class of Fractional Optimal Control Problems(World Scientific Publ Co Pte Ltd, 2022) Jafari, Hossein; Johnston, Sarah Jane; Baleanu, Dumitru; Firoozjaee, Mohammad ArabWe apply the Ritz method to approximate the solution of optimal control problems through the use of polynomials. The constraints of the problem take the form of differential equations of fractional order accompanied by the boundary and initial conditions. The ultimate goal of the algorithm is to set up a system of equations whose number matches the unknowns. Computing the unknowns enables us to approximate the solution of the objective function in the form of polynomials.Article Citation - WoS: 14Citation - Scopus: 15New Multi-Functional Approach for Κth-Order Differentiability Governed by Fractional Calculus Via Approximately Generalized (Ψ, (h)over-Bar) Functions in Hilbert Space(World Scientific Publ Co Pte Ltd, 2021) Wang, Miao-Kun; Rashid, Saima; Karaca, Yeliz; Baleanu, Dumitru; Chu, Yu-MingThis work addresses several novel classes of convex function involving arbitrary non-negative function, which is known as approximately generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex and approximately psi-quasiconvex function, with respect to Raina's function, which are elaborated in Hilbert space. To ensure the feasibility of the proposed concept and with the discussion of special cases, it is presented that these classes generate other classes of generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex functions such as higher-order strongly (HOS) generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex functions and HOS generalized psi-quasiconvex function. The core of the proposed method is a newly developed Simpson's type of identity in the settings of Riemann-Liouville fractional integral operator. Based on the HOS generalized (psi, PLANCK CONSTANT OVER TWO PI)-convex function representation, we established several theorems and related novel consequences. The presented results demonstrate better performance for HOS generalized psi-quasiconvex functions where we can generate several other novel classes for convex functions that exist in the relative literature. Accordingly, the assortment in this study aims at presenting a direction in the related fields.Article Citation - WoS: 2Citation - Scopus: 2Spectrum of the Q-Schrodinger Equation by Means of the Variational Method Based on the Discrete Q-Hermite I Polynomials(World Scientific Publ Co Pte Ltd, 2021) Turan, Mehmet; Adiguzel, Rezan Sevinik; Calisir, Ayse Dogan; Adlgüzel, Rezan Sevinik; Çallşlr, Ayşe DoǧanIn this work, the q-Schrodinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of q, and the limiting case as q -> 1 is considered. The Rayleigh-Ritz variational method is adopted to the system. The discrete q-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: q-harmonic, purely q-quartic and q-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.