Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Conference Object Citation - WoS: 4Citation - Scopus: 5On Hybrid Contractions Via Simulation Function in the Context of Quasi-Metric Spaces(Yokohama Publ, 2020) Karapinar, Erdal; Fulga, AndreeaIn this manuscript, we aim at investigating the existence of a fixed point theorem for the mappings that satisfy hybrid contraction in the setting of quasi-metric spaces. We provide examples to indicate the validity of the observed results.Editorial Citation - WoS: 0Citation - Scopus: 0Advanced Theoretical and Applied Studies of Fractional Differential Equations 2013(Hindawi Publishing Corporation, 2014) Baleanu, Dumitru; Trujillo, Juan J.; Ahmad, Bashir; MatematikCorrection Citation - WoS: 0Citation - Scopus: 0A Numerical Scheme for Two Dimensional Optimal Control Problems With Memory Effect (Vol 59, Pg 1630, 2010)(Pergamon-elsevier Science Ltd, 2010) Defterli, OzlemArticle Citation - WoS: 6Citation - Scopus: 7SOME SYMMETRIC PROPERTIES AND APPLICATIONS OF WEIGHTED FRACTIONAL INTEGRAL OPERATOR(World Scientific Publ Co Pte Ltd, 2023) Wu, Shanhe; Jarad, Fahd; Samraiz, Muhammad; Mehmood, Ahsan; Jarad, Fahd; Naheed, Saima; 234808; MatematikIn 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 Some more bounded and singular pulses of a generalized scale-invariant analogue of the Korteweg–de Vries equation(2023) Baleanu, Dumitru; Alqarni, M.M.; Ahmad, Shabir; Baleanu, Dumitru; Khan, Meraj Ali; Mahmoud, Emad E.; 56389; MatematikWe investigate a generalized scale-invariant analogue of the Korteweg–de Vries (KdV) equation, establishing a connection with the recently discovered short-wave intermediate dispersive variable (SIdV) equation. To conduct a comprehensive analysis, we employ the Generalized Kudryashov Technique (KT), Modified KT, and the sine–cosine method. Through the application of these advanced methods, a diverse range of traveling wave solutions is derived, encompassing both bounded and singular types. Among these solutions are dark and bell-shaped waves, as well as periodic waves. Significantly, our investigation reveals novel solutions that have not been previously documented in existing literature. These findings present novel contributions to the field and offer potential applications in various physical phenomena, enhancing our understanding of nonlinear wave equations.Article Citation - Scopus: 3Solving System of Fractional Differential Equations via Vieta-Lucas Operational Matrix Method(Springer, 2024) Chaudhary, R.; Baleanu, Dumitru; Aeri, S.; Bala, A.; Kumar, R.; Baleanu, D.; 56389; MatematikVieta-Lucas polynomials (VLPs) belong to the class of weighted orthogonal polynomials, which can be used to effectively handle various natural and engineered problems. The classical fractional derivative due to Caputo is used to write the emerging operational matrices. These matrices are developed and evaluated by using the properties of VLPs. The residuated functions are mapped to zero by the tools of the Tau algorithm. Convergence and error analysis are thoroughly explored. Test examples for a fractional system of differential equations are borrowed from literature. The theoretical and simulated exercise on these examples authenticate the relevance of this scheme. Here, novel inclusion of Vieta-Lucas polynomials has been ensured in combination with the Tau approach. The operational matrix approach which provides extensive information about the fractional derivatives of different terms of Vieta-Lucas polynomial expansion, is ensured to operate to reduce the problem into an algebraic setup. The novelty is further enhanced by comparing the present scheme with the fourth-order Runge–Kutta method. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.Article Citation - WoS: 8Citation - Scopus: 20Solving fractional integro-differential equations by Aboodh transform(int Scientific Research Publications, 2024) Raghavendran, Prabakaran; Baleanu, Dumitru; Gunasekar, Tharmalingam; Balasundaram, Hemalatha; Santra, Shyam Sundar; Majumder, Debasish; Baleanu, Dumitru; 56389; MatematikThis study approaches some families of fractional integro-differential equations (FIDEs) using a simple fractional calculus method, which leads to several appealing consequences, including the classical Frobenius method, which is generalized. The method presented here is based mostly on certain general theorems on particular solutions of FIDEs using the Aboodh transform and binomial series extension coefficients. We additionally demonstrate techniques to solve FIDEs.Article Citation - WoS: 8Citation - Scopus: 8Solitons of the (1 + 1) - and (2 + 1) -Dimensional Chiral Nonlinear Schrodinger Equations with the Jacobi Elliptical Function Method(Springer Basel Ag, 2023) Tala-Tebue, Eric; Baleanu, Dumitru; Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Korkmaz, Alper; 56389; MatematikOur objective is to find new analytical solutions of the (1+1)- and (2+1)-dimensional Chiral nonlinear Schrodinger (CNLS) equations using the Jacobi elliptical function method. The CNLS equations play a significant role in the development of quantum mechanics, particularly in the field of quantum Hall effect. Soliton solutions of the considered models are obtained such as, cnoidal solutions, the hyperbolic solutions and the trigonometric solutions. The obtained analytical solutions are new in the literature. The stability conditions of these solutions are also given. The obtained stable solutions are presented graphically for some specific parameters. Moreover, the conditions of modulational instability for both models are provided. The proposed method can be useful to obtain the analytical solutions of nonlinear partial differential equations.Article Solitary wave solutions to Gardner equation using improved tan(Ω(Υ)/2-expansion method(2023) Baleanu, Dumitru; Sadaf, Maasoomah; Dawood, Mirfa; Abbas, Muhammad; Baleanu, Dumitru; 56389; MatematikIn this study, the improved tan(Ω(Υ)/2-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.Article Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme(2022) Baleanu, Dumitru; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem; 56389; MatematikIn the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.Article Citation - WoS: 68Citation - Scopus: 76Recent developments of energy management strategies in microgrids: An updated and comprehensive review and classification(Pergamon-elsevier Science Ltd, 2023) Abbasi, Ali Reza; Baleanu, Dumitru; Baleanu, Dumitru; 56389; MatematikEnergy 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: 0Citation - Scopus: 0Quasilinear Coupled System in the Frame of Nonsingular ABC-Derivatives with p-Laplacian Operator at Resonance(Springer Basel Ag, 2024) Bouloudene, Mokhtar; Jarad, Fahd; Jarad, Fahd; Adjabi, Yassine; Panda, Sumati Kumari; 234808; MatematikWe investigate the existence of solutions for coupled systems of fractional p-Laplacian quasilinear boundary value problems at resonance given by the Atangana-Baleanu-Caputo (shortly, ABC) derivatives formulations are based on the well-known Mittag-Leffler kernel utilizing Ge's application of Mawhin's continuation theorem. Examples are provided to demonstrate our findings.Editorial Citation - WoS: 4Citation - Scopus: 3Preface to the Special Issue “A Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi”(Mdpi, 2023) Du, Wei-Shih; Agarwal, Ravi Prakash; Karapinar, Erdal; Kostic, Marko; Cao, Jian; 19184Article Citation - WoS: 4Citation - Scopus: 6Pathological study on uncertain numbers and proposed solutions for discrete fuzzy fractional order calculus(de Gruyter Poland Sp Z O O, 2023) Shiri, Babak; Baleanu, Dumitru; Baleanu, Dumitru; Ma, Chang-You; 56389; MatematikA pathological study in the definition of uncertain numbers is carried out, and some solutions are proposed. Fundamental theorems for uncertain discrete fractional and integer order calculus are established. The concept of maximal solution for obtaining a unique uncertain solution is introduced. The solutions of uncertain discrete relaxation equations for the integer and the fractional order are obtained. Various numerical examples are accompanied to clarify the theoretical results and study of uncertain system behavior.Article Citation - WoS: 1Citation - Scopus: 1Pachpatte type inequalities and their nabla unifications via convexity(indian Nat Sci Acad, 2024) Kayar, Zeynep; Kaymakçalan, Billur; Kaymakcalan, Billur; MatematikNabla unifications of the discrete and continuous Pachpatte type inequalities, which are convex generalizations of Hardy-Copson type inequalities, are established. These unifications also yield dual results, namely delta Pachpatte type inequalities. Some of the dual results and some discrete and continuous versions of nabla Pachpatte type inequalities have appeared in the literature for the first time.Article Citation - Scopus: 0Optimal control for a variable-order diffusion-wave equation with a reaction term; A numerical study(Elsevier B.V., 2024) Sweilam, N.H.; Baleanu, Dumitru; Megahed, F.; Shatta, S.A.; Baleanu, D.; 56389; MatematikIn this paper, optimal control for a variable-order diffusion-wave equation with a reaction term is numerically studied, where the variable-order operator is defined in the sense of Caputo proportional constant. Necessary optimality conditions for the control problem are derived. Existence and uniqueness for the solutions of fractional optimal control problem are derived. The nonstandard weighted average finite difference method and the nonstandard leap-frog method are developed to study numerically the proposed problem. Moreover, the stability analysis of the methods is proved. Finally, in order to characterise the memory property of the proposed model, three test examples are given. It is found that the nonstandard weighted average finite difference method can be applied to study such variable-order fractional optimal control problems simply and effectively. © 2024 The Author(s)Conference Object On Weighted Fractional Operators with Applications to Mathematical Models Arising in Physics(2023) Baleanu, Dumitru; Umer, Muhammad; Naheed, Saima; Baleanu, Dumitru; 56389; MatematikIn recent study, we develop the weighted generalized Hilfer-Prabhakar fractional derivative operator and explore its key properties. It unifies many existing fractional derivatives like Hilfer-Prabhakar and Riemann-Liouville. The weighted Laplace transform of the newly defined derivative is obtained. By involving the new fractional derivative, we modeled the free-electron laser equation and kinetic equation and then found the solutions of these fractional equations by applying the weighted Laplace transform.Article Citation - WoS: 14Citation - Scopus: 15On the multiparameterized fractional multiplicative integral inequalities(Springer, 2024) Almatrafi, Mohammed Bakheet; Jarad, Fahd; Saleh, Wedad; Lakhdari, Abdelghani; Jarad, Fahd; Meftah, Badreddine; 234808; MatematikWe introduce a novel multiparameterized fractional multiplicative integral identity and utilize it to derive a range of inequalities for multiplicatively s-convex mappings in connection with different quadrature rules involving one, two, and three points. Our results cover both new findings and established ones, offering a holistic framework for comprehending these inequalities. To validate our outcomes, we provide an illustrative example with visual aids. Furthermore, we highlight the practical significance of our discoveries by applying them to special means of real numbers within the realm of multiplicative calculus.Article Citation - WoS: 0Citation - Scopus: 0On the Maximal Subspaces of Discrete Hamiltonian Systems(Springernature, 2024) Ugurlu, Ekin; Uğurlu, Ekin; Bairamov, Elgiz; 238990; MatematikIn this paper, we consider a discrete Hamiltonian system on nonnegative integers, and using Sylvester's inertia indices theory, we construct maximal subspaces on which the Hermitian form has a certain sign. After constructing nested ellipsoids, we introduce a lower bound for the number of linearly independent summable-square solutions of the discrete equation. Finally, we provide a limit-point criterion.Article Citation - WoS: 10Citation - Scopus: 15On the decomposition and analysis of novel simultaneous SEIQR epidemic model(Amer inst Mathematical Sciences-aims, 2023) Umapathy, Kalpana; Baleanu, Dumitru; Palanivelu, Balaganesan; Jayaraj, Renuka; Baleanu, Dumitru; Dhandapani, Prasantha Bharathi; 56389; MatematikIn this manuscript, we are proposing a new kind of modified Susceptible Exposed Infected Quarantined Recovered model (SEIQR) with some assumed data. The novelty imposed here in the study is that we are studying simultaneously SIR, SEIR, SIQR, and SEQR pandemic models with the same data unchanged as the SEIQR model. We are taking this model a step ahead by using a non-helpful transition because it was mostly skipped in the literature. All sorts of features that are essential to study the models, such as basic reproduction number, stability analysis, and numerical simulations have been examined for this modified model with other models.
