Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
60 results
Search Results
Article Explicit Commutativity and Stability Theories for Second-Order Heun's LTVSs(World Scientific Publ Co Pte Ltd, 2025) Ibrahim, Salisu; Baleanu, DumitruThis paper derived and proved the simplex explicit commutativity theories and conditions for second-order linear time-varying systems (LTVSs) with both zero and nonzero initial conditions (ICs). We consider Heun's LTVS as a case study to verify the explicit commutative results, which were supported by simulation. Furthermore, we investigate the sensitivity of Heun's LTVS, the robustness of Heun's LTVS, the stability of Heun's LTVS, the effects due to disturbance on Heun's LTVS and the problem associated with commutativity of Heun's LTVS. These findings will tackle many problems related to the commutativity theory, the stability of LTVS, design and behavior of control systems, which have made an essential contribution and play a vital role in science and engineering. By considering a sinusoid of amplitude 5, bias -3 and frequency 7, with parameters c2,c1,c0 and an arbitrary choosing initial time (IT) t0 to be and also the initial states yA(0),yB(0),yA '(0),yB '(0), several quantitative results obtained by simulation show that the Heun's LTVSs AB and BA give the same output response, AB and BA are commutative under certain conditions and proved to be unstable numerically. Moreover, the quantitative results proved that the Heun's LTVSs AB and BA are very sensitive toward changes in ICs and parameters. Disturbance between the connections also affects the systems AB and BA, these give different responses as a result of tampering with the conditions, hence commutativity is not satisfied. Several examples have been given to support our fact explicitly and numerically. However, the explicit commutativity and stability for Heun's LTVS have not been in the literature yet, and this paper presents it for the first time. The results are well verified by simulation and treated with Wolfram Mathematica 11.Article Citation - WoS: 1A New Formulation and Analytical Applications of Fractional Operators(World Scientific Publ Co Pte Ltd, 2024) Mehmood, Ahsan; Samraiz, Muhammad; Liu, Zhi-Guo; Baleanu, Dumitru; Vivas-Cortez, MiguelThis research paper introduces a novel formulation of the modified Atangana-Baleanu (AB) Fractional Operators (FrOs). The paper begins by discussing the boundedness of the novel fractional derivative operator. Some fractional differential equations corresponding to different choices of functions as well as comparative graphical representations of a function and its derivative are provided. Furthermore, the paper investigates the generalized Laplace transform for this newly introduced operator. By employing the generalized Laplace transform, a wide range of fractional differential equations can be effectively solved. Additionally, the paper establishes the corresponding form of the AB Caputo fractional integral operator, examines its boundedness and obtains its Laplace transform. It is worth noting that the FrOs previously documented in the existing literature can be derived as special cases of these recently explored FrOs.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: 9Citation - Scopus: 11Monkeypox Viral Transmission Dynamics and Fractional-Order Modeling With Vaccination Intervention(World Scientific Publ Co Pte Ltd, 2023) Kumar, Sachin; Baleanu, Dumitru; Nisar, Kottakkaran sooppy; Singh, Jaskirat palA current outbreak of the monkeypox viral infection, which started in Nigeria, has spread to other areas of the globe. This affects over 28 nations, including the United Kingdom and the United States. The monkeypox virus causes monkeypox (MPX), which is comparable to smallpox and cowpox (MPXV). The monkeypox virus is a member of the Poxviridae family and belongs to the Orthopoxvirus genus. In this work, a novel fractional model for Monkeypox based on the Caputo derivative is explored. For the model, two equilibria have been established: disease-free and endemic equilibrium. Using the next-generation matrix and Castillo's technique, if R-0 < 1 the global asymptotic stability of disease-free equilibrium is shown. The linearization demonstrated that the endemic equilibrium point is locally asymptotically stable if R-0 > 1. Using the parameter values, the model's fundamental reproduction rates for both humans and non-humans are calculated. The existence and uniqueness of the solution are proved using fixed point theory. The model's numerical simulations demonstrate that the recommended actions will cause the infected people in the human and non-human populations to disappear.Article Citation - WoS: 22Citation - Scopus: 26Impact of Public Health Awareness Programs on Covid-19 Dynamics: a Fractional Modeling Approach(World Scientific Publ Co Pte Ltd, 2023) Yusuf, Abdullahi; Musa, Salihu s.; Qureshi, Sania; Alshomrani, Ali s.; Baleanu, Dumitru; Zafar, Zain ul abadinPublic health awareness programs have been a crucial strategy in mitigating the spread of emerging and re-emerging infectious disease outbreaks of public health significance such as COVID-19. This study adopts an Susceptible-Exposed-Infected-Recovered (SEIR) based model to assess the impact of public health awareness programs in mitigating the extent of the COVID-19 pandemic. The proposed model, which incorporates public health awareness programs, uses ABC fractional operator approach to study and analyze the transmission dynamics of SARS-CoV-2. It is possible to completely understand the dynamics of the model's features because of the memory effect and hereditary qualities that exist in the fractional version. The fixed point theorem has been used to prove the presence of a unique solution, as well as the stability analysis of the model. The nonlinear least-squares method is used to estimate the parameters of the model based on the daily cumulative cases of the COVID-19 pandemic in Nigeria from March 29 to June 12, 2020. Through the use of simulations, the model's best-suited parameters and the optimal ABC fractional-order parameter t may be determined and optimized. The suggested model is proved to understand the virus's dynamical behavior better than the integer-order version. In addition, numerous numerical simulations are run using an efficient numerical approach to provide further insight into the model's features.Article Citation - WoS: 16Citation - Scopus: 15Fractional Hyper-Chaotic System With Complex Dynamics and High Sensitivity: Applications in Engineering(World Scientific Publ Co Pte Ltd, 2024) Yusuf, Abdullahi; Alshomrani, Ali S. S.; Sulaiman, Tukur Abdulkadir; Baleanu, Dumitru; Partohaghighi, MohammadHyper-chaotic systems have useful applications in engineering applications due to their complex dynamics and high sensitivity. This research is supposed to introduce and analyze a new noninteger hyper-chaotic system. To design its fractional model, we consider the Caputo fractional operator. To obtain the approximate solutions of the extracted system under the considered fractional-order derivative, we employ an accurate nonstandard finite difference (NSFD) algorithm. Moreover, the existence and uniqueness of the solutions are provided using the theory of fixed-point. Also, to see the performance of the utilized numerical scheme, we choose different values of fractional orders along with various amounts of the initial conditions (ICs). Graphs of solutions for each case are provided.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: 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: 105Citation - Scopus: 118On an Extension of the Operator With Mittag-Leffler Kernel(World Scientific Publ Co Pte Ltd, 2022) Baleanu, Dumitru; Al-Refai, MohammedDealing with nonsingular kernels is not an easy task due to their restrictions at origin. In this short paper, we suggest an extension of the fractional operator involving the Mittag-Leffler kernel which admits integrable singular kernel at the origin. New solutions of the related differential equations were reported together with some perspectives from the modelling viewpoint.