Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
Browse
Recent Submissions
Item Citation Count: Wu, Shanhe...et al (2023). "SOME SYMMETRIC PROPERTIES AND APPLICATIONS OF WEIGHTED FRACTIONAL INTEGRAL OPERATOR", Fractals, Vol. 31, No. 10.SOME SYMMETRIC PROPERTIES AND APPLICATIONS OF WEIGHTED FRACTIONAL INTEGRAL OPERATOR(2023) Wu, Shanhe; Samraiz, Muhammad; Mehmood, Ahsan; Jarad, Fahd; Naheed, Saima; 234808; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüIn 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.Item Citation Count: Saifullah, Sayed...et al (2023). "Some more bounded and singular pulses of a generalized scale-invariant analogue of the Korteweg–de Vries equation", Results in Physics, Vol. 52.Some more bounded and singular pulses of a generalized scale-invariant analogue of the Korteweg–de Vries equation(2023-09) Saifullah, Sayed; Alqarni, M.M.; Ahmad, Shabir; Baleanu, Dumitru; Khan, Meraj Ali; Mahmoud, Emad E.; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüWe 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.Item Citation Count: Chaudhary, Rahul...et al (2024). "Solving System of Fractional Differential Equations via Vieta-Lucas Operational Matrix Method", International Journal of Applied and Computational Mathematics, Vol. 10, No. 1.Solving System of Fractional Differential Equations via Vieta-Lucas Operational Matrix Method(2024-02) Chaudhary, Rahul; Aeri, Shivani; Bala, Anu; Kumar, Rakesh; Baleanu, Dumitru; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüVieta-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.Item Citation Count: Raghavendran, Prabakaran...et al (2024). "Solving fractional integro-differential equations by Aboodh transform", Journal of Mathematics and Computer Science, Vol. 32, No. 3, pp. 229-240.Solving fractional integro-differential equations by Aboodh transform(2024) Raghavendran, Prabakaran; Gunasekar, Tharmalingam; Balasundaram, Hemalatha; Santra, Shyam Sundar; Majumder, Debasish; Baleanu, Dumitru; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüThis 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.Item Citation Count: Tala-Tebue, Eric...et al (2023). "Solitons of the (1 + 1) - and (2 + 1) -Dimensional Chiral Nonlinear Schrodinger Equations with the Jacobi Elliptical Function Method", Qualitative Theory of Dynamical Systems, Vol. 22, No. 3.Solitons of the (1 + 1) - and (2 + 1) -Dimensional Chiral Nonlinear Schrodinger Equations with the Jacobi Elliptical Function Method(2023-09) Tala-Tebue, Eric; Rezazadeh, Hadi; Javeed, Shumaila; Baleanu, Dumitru; Korkmaz, Alper; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüOur 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.Item Citation Count: Akram, Ghazala...et al (2023). "Solitary wave solutions to Gardner equation using improved tan(Ω(Υ)/2-expansion method", AIMS Mathematics, Vol. 8, No. 2, pp. 4390-4406.Solitary wave solutions to Gardner equation using improved tan(Ω(Υ)/2-expansion method(2023) Akram, Ghazala; Sadaf, Maasoomah; Dawood, Mirfa; Abbas, Muhammad; Baleanu, Dumitru; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüIn 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.Item Citation Count: Ranjbar, Hassan...et al (2022). "Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme", AIMS MATHEMATICS, Vol. 8, No. 2, pp. 2576-2590.Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme(2022) Ranjbar, Hassan; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, Kazem; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüIn 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.Item Citation Count: Abbasi, Ali Reza; Baleanu, Dumitru (2023). "Recent developments of energy management strategies in microgrids: An updated and comprehensive review and classification", Energy Conversion and Management, Vol. 297.Recent developments of energy management strategies in microgrids: An updated and comprehensive review and classification(2023-12-01) Abbasi, Ali Reza; Baleanu, Dumitru; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüEnergy 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° 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.Item Citation Count: Bouloudene, Mokhtar...et al (2024). "Quasilinear Coupled System in the Frame of Nonsingular ABC-Derivatives with p-Laplacian Operator at Resonance", Qualitative Theory of Dynamical Systems, Vol. 23, no. 1.Quasilinear Coupled System in the Frame of Nonsingular ABC-Derivatives with p-Laplacian Operator at Resonance(2024-02) Bouloudene, Mokhtar; Jarad, Fahd; Adjabi, Yassine; Panda, Sumati Kumari; 234808; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüWe 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.Item Citation Count: Du, Wei-Shih...et al (2023). "Preface to the Special Issue “A Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi”", Axioms, Vol. 12, No. 9.Preface to the Special Issue “A Themed Issue on Mathematical Inequalities, Analytic Combinatorics and Related Topics in Honor of Professor Feng Qi”(2023-09) Du, Wei-Shih; Agarwal, Ravi Prakash; Karapinar, Erdal; Kostić, Marko; Cao, Jian; 19184; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüItem Citation Count: Shiri, Babak; Baleanu, Dumitru; Ma, Chang-You (2023). "Pathological study on uncertain numbers and proposed solutions for discrete fuzzy fractional order calculus", Open Physics, Vol. 21, No. 1.Pathological study on uncertain numbers and proposed solutions for discrete fuzzy fractional order calculus(2023-01-01) Shiri, Babak; Baleanu, Dumitru; Ma, Chang-You; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüA 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.Item Citation Count: Kayar, Zeynep; Kaymakçalan, Billur (2024). "Pachpatte type inequalities and their nabla unifications via convexity", Indian Journal of Pure and Applied Mathematics.Pachpatte type inequalities and their nabla unifications via convexity(2024) Kayar, Zeynep; Kaymakçalan, Billur; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüNabla 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.Item Citation Count: Sweilam, N.H...et al (2024). "Optimal control for a variable-order diffusion-wave equation with a reaction term; A numerical study", Partial Differential Equations in Applied Mathematics, Vol. 10.Optimal control for a variable-order diffusion-wave equation with a reaction term; A numerical study(2024-06) Sweilam, N.H.; Megahed, F.; Shatta, S.A.; Baleanu, Dumitru; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüIn 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.Item Citation Count: Samraiz, Muhammad...et al (2023). "On Weighted Fractional Operators with Applications to Mathematical Models Arising in Physics", Lecture Notes in Networks and Systems, 5th International Conference On Mathematical Modelling, Applied Analysis And Computation, ICMMAAC 2022, Vol. 666, pp. 53-68.On Weighted Fractional Operators with Applications to Mathematical Models Arising in Physics(2023) Samraiz, Muhammad; Umer, Muhammad; Naheed, Saima; Baleanu, Dumitru; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüIn 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.Item Citation Count: Almatrafi, Mohammed Bakheet...et al.(2024). "On the multiparameterized fractional multiplicative integral inequalities", Journal of Inequalities and Applications, Vol. 2024, No. 1.On the multiparameterized fractional multiplicative integral inequalities(2024-12) Almatrafi, Mohammed Bakheet; Saleh, Wedad; Lakhdari, Abdelghani; Jarad, Fahd; 234808; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüWe 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.Item Citation Count: Uğurlu, Ekin; Bairamov, Elgiz (2024). "On the Maximal Subspaces of Discrete Hamiltonian Systems", Bulletin of the Malaysian Mathematical Sciences Society, Vol. 47, No. 3.On the Maximal Subspaces of Discrete Hamiltonian Systems(2024-05) Uğurlu, Ekin; Bairamov, Elgiz; 238990; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüIn 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.Item Citation Count: Umapathy, Kalpana...et al.(2023). "On the decomposition and analysis of novel simultaneous SEIQR epidemic model", AIMS Mathematics, Vol. 8, No. 3, pp. 5918-5933.On the decomposition and analysis of novel simultaneous SEIQR epidemic model(2023) Umapathy, Kalpana; Palanivelu, Balaganesan; Jayaraj, Renuka; Baleanu, Dumitru; Dhandapani, Prasantha Bharathi; 56389; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüIn 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 SEIQR model with decomposed other epidemic models. © 2023 the Author(s), licensee AIMS Press.Item Citation Count: Kayar, Zeynep; Kaymakçalan, Billur (2024). "On the complementary nabla Pachpatte type dynamic inequalities via convexity", Kuwait Journal of Science, Vol. 51, No. 1.On the complementary nabla Pachpatte type dynamic inequalities via convexity(2024-01) Kayar, Zeynep; Kaymakçalan, Billur; 109448; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüPachpatte type inequalities are convex generalizations of the well-known Hardy-Copson type inequalities. As Hardy-Copson type inequalities and convexity have numerous applications in pure and applied mathematics, combining these concepts will lead to more significant applications that can be used to develop certain branches of mathematics such as fuctional analysis, operator theory, optimization and ordinary/partial differential equations. We extend classical nabla Pachpatte type dynamic inequalities by changing the interval of the exponent δ from δ > 1 to δ < 0. Our results not only complement the classical nabla Pachpatte type inequalities but also generalize complementary nabla Hardy-Copson type inequalities. As the case of δ < 0 has not been previously examined, these complementary inequalities represent a novelty in the nabla time scale calculus, specialized cases in continuous and discrete scenarios, and in the dual outcomes derived in the delta time scale calculus.Item Citation Count: Bairamov, Elgiz; Taş, Kenan; Uğurlu, Ekin (2024). "On the characteristic functions and Dirchlet-integrable solutions of singular left-definite Hamiltonian systems", Quaestiones Mathematicae, Vol. 47, No. 5, pp. 983-995.On the characteristic functions and Dirchlet-integrable solutions of singular left-definite Hamiltonian systems(2024) Bairamov, Elgiz; Taş, Kenan; Uğurlu, Ekin; 238990; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüIn this work, a singular left-definite Hamiltonian system is considered and the characteristic-matrix theory for this Hamiltonian system is constructed. Using the results of this theory we introduce a lower bound for the number of Dirichlet-integrable solutions. Moreover we share a relation between the kernel of the solution of the nonhomogeneous boundary value problem and the characteristic-matrix.Item Citation Count: Uğurlu, Ekin (2024). "On some even-sequential fractional boundary-value problems", Fractional Calculus and Applied Analysis, Vol. 27, No. 1, pp. 353-392.On some even-sequential fractional boundary-value problems(2024-02) Uğurlu, Ekin; 238990; Çankaya Üniversitesi, Fen - Edebiyat Fakültesi, Matematik BölümüIn this paper we provide a way to handle some symmetric fractional boundary-value problems. Indeed, first, we consider some system of fractional equations. We introduce the existence and uniqueness of solutions of the systems of equations and we show that they are entire functions of the spectral parameter. In particular, we show that the solutions are at most of order 1/2. Moreover we share the integration by parts rule for vector-valued functions that enables us to obtain some symmetric equations. These symmetries allow us to handle 2 - sequential and 4 - sequential fractional boundary-value problems. We provide some expansion formulas for the bilinear forms of the solutions of 2 - sequential and 4 - sequential fractional equations which admit us to impose some unusual boundary conditions for the solutions of fractional differential equations. We show that the systems of eigenfunctions of 2 - sequential and 4 - sequential fractional boundary value problems are complete in both energy and mean. Furthermore, we study on the zeros of solutions of 2 - sequential fractional differential equations. At the end of the paper we show that 6 - sequential fractional differential equation can also be handled as a system of equations and hence almost all the results obtained in the paper can be carried for such boundary-value problems.