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https://hdl.handle.net/20.500.12451/122

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An Improved Numerical Solution of Modified Regularized Long Wave Equation by Quartic Trigonometric B-Spline
(10.1007/s40819-025-01832-x, 2025) Kirli, Emre; Mersin, Mehmet Ali
This study presents the application of a numerical method specifically designed to solve the Modified Regularized Long Wave equation, a crucial model in the analysis of non-linear wave dynamics. The proposed method employs a Quartic Trigonometric B-spline approach for spatial discretization, which ensures smooth and accurate interpolation across the spatial domain, while temporal integration is conducted using the well-established fourth-order Runge–Kutta (RK4) scheme, known for its stability and precision. To evaluate the performance of the method, it is applied to three test problems: the propagation of a single solitary wave, the interaction between two and three solitary waves. The invariant quantities are computed for all test cases. To ensure the stability of the method, a stability analysis is performed through the computation of eigenvalues. The results demonstrate that the proposed method achieves a high degree of accuracy in preserving the invariant properties and produces minimal error, highlighting its efficiency and reliability.
A high order accurate hybrid technique for numerical solution of modified equal width equation
(Elsevier B.V., 2025) Kirli, Emre; Cıkıt, Serpil
In this present study, a high-order accurate hybrid technique is developed to establish the approximate solution of Modified Equal Width (MEW) equation which is used to define solitary waves. The spatial integration is based on combining the cubic B-spline and a fourth-order compact finite-difference (FOCFD) scheme, while the temporal integration is carried out by using fourth-order Runge–Kutta (RK4) scheme. In present technique, the new approximation for the spatial second derivative is constructed by the FOCFD scheme in which the spatial second derivatives of unknowns can be written in terms of the unknowns themselves and their first derivatives. Hence, the spatial second derivative reaches the accuracy of order four, while it is represented by the accuracy of order two in the standard cubic B-spline. The stability of the suggested technique is discussed by using the concept of eigenvalue. Three test problems are examined to verify the efficiency and applicability of the suggested technique. The computed results are compared with the other numerical results in previous works. The comparisons reveal that the suggested hybrid technique provides better results with high accuracy and minimum computational effort.
Comparision of Conformable and Caputo fractional grey models
(Elsevier B.V., 2025) Bilgil, Halis; Yüksel, Simge
In recent years, fractional order derivatives have been encountered in various fields of science, particularly in applied mathematics. Although there are many fractional derivative definitions in the literature, there are very few studies on which derivative definition works better in a mathematical model. In applications, it is seen that calculations are easier with the model using the Conformable derivative operator due to the simplicity of the derivative definition. However, the Caputo derivative operator, which is considered to be more effective in models related to time series due to its memory property, leads to more complex calculations. In this article, two fractional grey models were created in the same structure with Conformable and Caputo derivative operators and their applications were implemented on the same data sets to a performance comparison of the fractional operators. The working mechanisms of fractional grey models constructed with both Caputo and Conformable derivative operators were demonstrated in detail. Solution of the whitening differential equation in the Caputo fractional grey model was obtained using Laplace transforms. Here, Conformable and Caputo fractional grey models were applied to the forecast of three real time series and their forecast performances were compared. Data on China's annual domestic energy consumption, annual wind energy consumption, and areas affected by drought disasters were utilized as real-time series. It has been observed that Conformable fractional grey models provide more accurate predictions with lower errors for certain datasets, while Caputo fractional grey models demonstrate better performance for others. This study is the first study in the literature that compared the Conformable and Caputo derivative operators on a grey model.
Pseudosymmetric Almost α-Cosymplectic (κ, μ, v)-Spaces Admitting Einstein Solitons
(RGN Publications, 2024) Atçeken, Mehmet; Mert, Tuğba; Uygun, Pakize
This paper attempts to characterize cases of an almost alpha alpha-cosymplectic (kappa, mu, nu)-space admitting Einstein sloitons to be concircular Ricci pseudosymmetry, projective Ricci pseudosymmetry, W-1-curvature and the W-2-curvature Ricci pseudo symmetric.
Invariant pseudoparallel submanifolds of an almost α-cosymplectic (κ, μ, ν)- space
(Honam Mathematical Journal, 2024) Atçeken, Mehmet; Yüca, Gülsüm
In this article, we research the conditions for invariant sub- manifolds in an almost alpha- cosymplectic ( kappa, mu, v ) space to be pseudo-parallel, Ricci-generalized pseudo-parallel and 2-Ricci-generalized pseudo-parallel. We think that the results for the relations among the functions will contribute to differential geometry.
α, β)-type almost η-Ricci-Yamabe solitions in perfect fluid spacetime
(Comenius University in Bratislava, 2024) Pandey, Shashikant; Mert, Tuğba; Atçeken, Mehmet
In this paper, we consider perfect fluid spacetime admitting (α, β)-type almost η-Ricci–Yamabe solitons by means of some curvature tensors. Ricci pseudosymmetry concepts of perfect fluid spacetime admitting (α, β)-type almost η-Ricci–Yamabe soliton are introduced according to the choice of some special curvature tensors such as Riemann, concircular and projective curvature tensor. After then, according to choosing of the curvature tensors, necessary conditions are given for perfect fluid spacetime admitting (α, β)-type almost η-Ricci–Yamabe soliton to be Ricci semisymmetric. Then, some important characterizations are given for Ricci, Yamabe, Einstein and η-Einstein solitons on perfect fluid spacetime.
Some characterizations for a (k, µ)-paracontact metric manifold to be an η-Einstein manifold
(Palestine Polytechnic University, 2024) Uygun, Pakize; Atçeken, M.
In this paper we introduce the curvature tensors of (k,µ)-paracontact manifold satisfying the conditions (formula presented) According these cases, (k, µ)-paracontact manifolds have been characterized such as η-Einstein.
On circulant and r-circulant matrices with Ducci sequences and Lucas numbers
(University of Nis, 2024) Yağmur, Tülay
A Ducci sequence is a sequence {S, DS, D2S, …}, where the map D: ℤn → ℤn takes each S = (s1, s2, s3, …, sn−1, sn) to (|s1 − s2 |, |s2 − s3 |, …, |sn−1 − sn |, |sn − s1 |). In this paper, we study norms of r-circulant matrices Circr (DL) and Circr (D2L), where L is an n-tuple of Lucas numbers. Then we examine some properties of circulant matrices Circ(DL) and Circ(D2L).
A study on pseudoparallel submanifolds of generalized Lorentz-Sasakian space forms
(University of Nis, 2024) Pandey, Shashikant; Mert, Tuğba; Atçeken, Mehmet; Uygun, Pakize
In this article, pseudoparallel submanifolds for generalized Lorentz-Sasakian space forms are investigated. Submanifolds of these manifolds with properties such as pseudoparallel, 2-pseudoparallel, Ricci generalized pseudoparallel, and 2-Ricci generalized pseudoparallel have been investigated and the conditions under which these pseudoparallel submanifolds are totally geodesic are shown. In addition, necessary and sufficient conditions have been obtained for these submanifolds to be totally geodesic by means of the concircular, projective and quasi-conformally curvature tensors. At last, we provide an example for such manifold.
Lorentz-Sasakian space forms on w0 ?curvature tensor
(Palestine Polytechnic University, 2024) Mert, T.; Atçeken, M.
In this article, Lorentz-Sasakian space forms on W0-curvature tensor are investigated. Riemann, Ricci, concircular, and projective curvature tensors are discussed for (2m + 1)dimensional Lorentz-Sasakian space forms, and with the help of these curvature tensors, some special curvature conditions established on the W0-curvature tensor are examined. Also, with the help of these curvature conditions, some properties of Lorentz-Sasakian space forms such as Einstein manifold, ?-Einstein manifold, and real space form have been obtained.
Certain Results for Invariant Submanifolds of an Almost ?-Cosymplectic (k, µ, ?)-Space
(Murat TOSUN, 2024) Uygun, Pakize; Atçeken, Mehmet; Mert, Tuğba
In this paper we present invariant submanifolds of an almost ?-cosymplectic (k, µ, ?)-space. Then, we gave some results for an invariant submanifold of an almost ?-cosymplectic (k, µ, ?)-space to be totally geodesic. As a result, we have discovered some interesting conclusions about invariant submanifolds of an almost cosymplectic (k, µ, ?)-space.
Invariant and Anti-Invariant Submanifolds of Generalized Sasakian Space Forms
(Pleiades Publishing, 2024) Mert, T.; Pandey, S.; Atçeken, M.; De, U.C.
In this article, invariant and anti-invariant submanifolds of generalized Sasakian space forms are investigated. The important properties of such submanifolds are determined according to both Levi-Civita connection and semisymmetric metric connection. Characterizations of Ricci solitons have researched according to Levi-Civita connection and semisymmetric metric connection on invariant and anti-invariant submanifolds of generalized Sasakian space form.
From cssc-crossed modules to categorical groups
(Tbilisi Centre for Mathematical Sciences, 2024) Datuashvili, Tamar; Mucuk, Osman; Alemdar, Nazmiye; Şahan, Tunçar
For any cssc-crossed module a category is constructed, equipped with a structure and proved that this is a coherent categorical group. Together with a result of the previous paper, where to any categorical group the cssc-crossed module is associated, this construction will enable us to prove an equivalence between the categories of categorical groups and of cssc-crossed modules in the sequel to this paper.
Non-Newtonian Pell and Pell-Lucas numbers
(Tokat Gaziosmanpaşa Üniversitesi, 2024) Yağmur, Tülay
In the present paper, we introduce a new type of Pell and Pell-Lucas numbers in terms of non-Newtonian calculus, which we call non-Newtonian Pell and non-Newtonian Pell-Lucas numbers, respectively. In non-Newtonian calculus, we study some significant identities and formulas for classical Pell and Pell-Lucas numbers. Therefore, we derive some relations with non-Newtonian Pell and Pell-Lucas numbers. Furthermore, we investigate some properties of non-Newtonian Pell and Pell-Lucas numbers, including Catalan-like identities, Cassini-like identities, Binet-like formulas, and generating functions.
Hyper-Dual Leonardo Quaternions
(Naim Çağman, 2024) Yağmur, Tülay
In this paper, hyper-dual Leonardo quaternions are defined and studied. Some basic properties of the hyper-dual Leonardo quaternions, including their relationships with the hyper-dual Fibonacci quaternions and hyper-dual Lucas quaternions, are analyzed. In addition, some formulae and identities, such as the recurrence relations, Binet's formula, generating functions, Vajda's identity, certain sum formulae, and some binomial-sum formulae, are investigated for hyper-dual Leonardo quaternions.
(?, ?)-TYPE ALMOST ?-RICCI–YAMABE SOLITONS IN PERFECT FLUID SPACETIME
(Comenius University in Bratislava, 2024) Pandey, Shashikant; Mert, Tuğba; Atçeken, Mehmet
In this paper, we consider perfect fluid spacetime admitting (?, ?)-type almost ?-Ricci–Yamabe solitons by means of some curvature tensors. Ricci pseudosymmetry concepts of perfect fluid spacetime admitting (?, ?)-type almost ?-Ricci–Yamabe soliton are introduced according to the choice of some special curvature tensors such as Riemann, concircular and projective curvature tensor. After then, according to choosing of the curvature tensors, necessary conditions are given for perfect fluid spacetime admitting (?, ?)-type almost ?-Ricci–Yamabe soliton to be Ricci semisymmetric. Then, some important characterizations are given for Ricci, Yamabe, Einstein and ?-Einstein solitons on perfect fluid spacetime.
New approach for investigating a class of multi-cost interval-valued extremization problems
(Multidisciplinary Digital Publishing Institute (MDPI), 2024) Trean??, Savin; Özgül, Emine
This study concentrates on a new approach for solving a class of multi-cost convex interval-valued extremization problems. Namely, we apply the weighting technique to find efficient solutions to these problems, defined in terms of (Formula presented.) -efficiency and weak (Formula presented.) -efficiency. Thus, an auxiliary weighting extremization problem related to the considered multi-cost interval-valued extremization problem is introduced. Under appropriate convexity hypotheses, an equivalence is established between the (weakly) (Formula presented.) -efficient solution of the multi-cost interval-valued extremization problem and the optimal solution of the auxiliary weighting extremization problem. Also, a numerical example is formulated to support the theoretical developments derived in the paper.
A note on P-Sasakian manifolds satisfying certain conditions
(Universidad Catolica del Norte, 2024) Uygun, Pakize; Atçeken, Mehmet
In the present paper, we have studied the curvature tensors of P-Sasakian manifold. For a P-Sasakian manifold, (Formula presented) and W9 · W1 = 0 cases are considered. According these cases, P-Sasakian manifolds have been characterized such as ?-Einstein and Einstein. In addition, we research W1-flat and W9-flat for a P-Sasakian manifold. The results are interesting and give an idea about the geometry of P-Sasakian manifold.
A novel fractional forecasting model for time dependent real world cases
(National Statistical Institute, 2024) Erdinç, Ümmügülsüm; Bilgil, Halis; Öztürk, Zafer
The grey modelling in the prediction of time series has been one of the interesting study fields recently due to its efficiency and convenience. Fractional grey models, on the other hand, have become preferable, despite the difficulty in calculations, since they give more effective results than standard models. Difficulties in fractional accumulation and difference calculations have begun to be overcome thanks to new definitions and theorems made in recent years. The new trend in grey modelling is to compose models that are more useful than the previous ones and give results with less error. In this paper, a new grey model derived from the conformable fractional order is defined and it is shown that more effective estimates are made compared to the models created in recent years. The verification of the method is shown with real data set. The results show that the proposed conformable fractional grey model is more effective than the existing models.
Novel algorithms based on forward-backward splitting technique: effective methods for regression and classification
(Springer, 2024) Atalan, Yunus; Hacıoğlu, Emirhan; Ertürk, Müzeyyen; Gürsoy, Faik; Milovanovi?, Gradimir V.
In this paper, we introduce two novel forward-backward splitting algorithms (FBSAs) for nonsmooth convex minimization. We provide a thorough convergence analysis, emphasizing the new algorithms and contrasting them with existing ones. Our findings are validated through a numerical example. The practical utility of these algorithms in real-world applications, including machine learning for tasks such as classification, regression, and image deblurring reveal that these algorithms consistently approach optimal solutions with fewer iterations, highlighting their efficiency in real-world scenarios.

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