Browsing by Author "Cekim, Bayram"

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Finite Bivariate Biorthogonal I-Konhauser Polynomials
(Elsevier, 2026) Lekesiz, Esra Guldogan; Cekim, Bayram; Ozarslan, Mehmet Ali
In the present study, a finite set of biorthogonal polynomials in two variables, produced from Konhauser polynomials, is introduced. Some properties like Laplace transform, integral and operational representation, fractional calculus operators of this family are investigated. Also, we compute Fourier transform for this new set and discover a new family of finite biorthogonal functions with the help of Parseval's identity. Further, in order to have semigroup property, we modify this finite set by adding two new parameters and construct fractional calculus operators. Thus, integral equation and integral operator are obtained for the modified version.
Citation - WoS: 1
Citation - Scopus: 1
On the Quantitative Weighted Generalization of Jafari Transform
(Univ Nis, Fac Sci Math, 2025) Yazici, Serdal; Cekim, Bayram; Jarad, Fahd; Jafari, Hossein
In this paper, a quantitative weighted transform based on the Jafari transform is proposed, and the mathematical foundations of this new transform are investigated. In the first section, some information about Jafari transform and some mathematical tools are reviewed. In the second section, the quantitative weighted Jafari transform is introduced, its existence guaranteed through a theorem, and its fundamental properties are examined. Additionally, transforms of the fractional derivative and fractional integral of a function with respect to a function h and a w-weight are obtained. In the third section, the theoretical findings are applied to solve classical and fractional initial value problems based on a function h and w-weight. In the last section, the results are discussed.