Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Finite Biorthogonal Polynomials Suggested by the Finite Orthogonal Polynomials Mnp,Qx(Wiley, 2026) Guldogan Lekesiz, EsraConstructing a biorthogonal structure from scratch, that is, defining a biorthogonal pair is quite tough. Because here the orthogonality must be established between two different sets. There are four known univariate biorthogonal polynomial sets, suggested by Laguerre, Jacobi, Hermite and Szeg & odblac;-Hermite polynomials, in the literature. In this paper, we derive for the first time a pair of finite univariate biorthogonal polynomials suggested by the finite univariate orthogonal polynomials . The corresponding biorthogonality relation and some useful relations and properties, including differential equation and generating function, are presented. Further, a new family of finite biorthogonal functions is obtained using Fourier transform and Parseval identity. In addition, we compute the Laplace transform and fractional calculus operators for the new biorthogonal polynomial set .Article Citation - Scopus: 1On The Problem Of Schoenberg On Rn(University of Prishtina, 2024) Kushpel, Alexander; Taş, KenanArticle Citation - WoS: 13Citation - Scopus: 16A Generalized Study of the Distribution of Buffer Over Calcium on a Fractional Dimension(Taylor & Francis Ltd, 2023) Jangid, Kamlesh; Kumawat, Shyamsunder; Purohit, Sunil Dutt; Baleanu, Dumitru; Suthar, D. L.; Bhatter, SanjayCalcium is an essential element in our body and plays a vital role in moderating calcium signalling. Calcium is also called the second messenger. Calcium signalling depends on cytosolic calcium concentration. In this study, we focus on cellular calcium fluctuations with different buffers, including calcium-binding buffers, using the Hilfer fractional advection-diffusion equation for cellular calcium. Limits and start conditions are also set. By combining with intracellular free calcium ions, buffers reduce the cytosolic calcium concentration. The buffer depletes cellular calcium and protects against toxicity. Association, dissociation, diffusion, and buffer concentration are modelled. The solution of the Hilfer fractional calcium model is achieved through utilizing the integral transform technique. To investigate the influence of the buffer on the calcium concentration distribution, simulations are done in MATLAB 21. The results show that the modified calcium model is a function of time, position, and the Hilfer fractional derivative. Thus the modified Hilfer calcium model provides a richer physical explanation than the classical calcium model.