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

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Fractional integral inequalities for s-convex functions in the first sense
(Taylor and Francis Ltd., 2025) Tınaztepe, Gültekin; Yeşilce Işık, İlknur
Certain fractional integral inequalities via general fractional integral operator are presented for s-convex functions in the first sense. Also, they are restated in terms of the Riemann-Liouville and Hadamard fractional integrals and illustrated.
Separation and connectedness in the category of constant filter convergence spaces
(University of Nis, 2025) Erciyes, Ayhan; Baran, Tesnim Meryem
The purpose of this work is to introduce two notions of closure in the category ConFCO of constant filter convergence spaces with continuous maps and investigate whether they satisfy the idempotency, productivity, (weak) hereditariness, and (full) additiveness as well as examine how they are related to each other. Moreover, we characterize each of Ti, i = 1, 2 spaces with respect to these closures and examine epimorphisms in the subcategories of ConFCO. Furthermore, we give the characterization of connected constant filter convergence spaces and investigate some invariance properties of them. Finally, we compare our results with results in some other topological categories.
Applications of the Tachibana operator on invariant submanifolds of Lorentzian Trans-Sasakian manifolds
(University of Nis, 2025) Atçeken, Mehmet; Mert, Tuğba; Stanković, Mića S.
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New insights on pseudoparallel submanifold in trans Sasakian manifolds
(University of Nis, 2025) Atçeken, Mehmet; Mert, Tuğba; Uygun, Pakize; Stanković, Mića S.
The aim of the present paper is to study invariant pseudo-parallel submanifolds of a trans Sasakian manifold. We have searched the necessary and sufficient conditions for an invariant pesudo-parallel submanifold to be totally geodesic under the some conditions.
Novel escape criteria for complex-valued hyperbolic functions through a fixed point iteration method
(American Institute of Mathematical Sciences, 2025) Şahan, Tunçar; Atalan, Yunus
This study presented an efficient fixed-point iteration method for deriving novel escape criteria for hyperbolic sine and hyperbolic cosine functions of varying degrees. The method contributes to obtaining more accurate and effective escape criteria, thereby enhancing the mathematical understanding and computational analysis of these functions. Additionally, using the derived criteria, the iteration method was employed to generate visually appealing fractals for Julia and Mandelbrot sets, demonstrating significant advantages in computational speed and practical utility. The method’s effective performance in producing complex and aesthetically satisfying fractal structures highlights its efficiency and applicability in fractal generation.
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.

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