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 .Conference Object The Generalized Finite Bivariate Biorthogonal M-Jacobi Polynomials(Springer, 2026) Çekim, Bayram; Özarslan, Mehmet Ali; Güldoğan Lekesiz, EsraArticle Citation - Scopus: 1On The Problem Of Schoenberg On Rn(University of Prishtina, 2024) Kushpel, Alexander; Taş, KenanArticle Citation - Scopus: 1Finite Bivariate Biorthogonal I-Konhauser Polynomials(Elsevier, 2026) Lekesiz, Esra Guldogan; Cekim, Bayram; Ozarslan, Mehmet Ali; Güldoğan Lekesi̇z, EsraIn 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.Article Recent Advances in Special Functions, Fractional Operators and Their Real World Applications(Cambridge Scientific Publishers, 2021) Singh, J.; Baleanu, Dumitru; Baleanu, D.; Kumar, D.; Hammouch, Z.; MatematikThis special issue ”Recent Advances in Special Functions, Fractional Operators and their Real World Applications” of the journal Mathematics in Engineering, Science and Aerospace (MESA) is mainly collection of the research articles presented in 3rd International Conference on Mathematical Mod-elling, Applied Analysis and Computation (ICMMAAC-20) organized by the Department of Mathe-matics, JECRC University, Jaipur, India during August 7-9, 2020. This collection of articles is mainly concerned to address a wide range of special functions, operators of fractional order and their uses in mathematical modelling and computation of distinct problems of physical sciences, chemical sci-ences, biological sciences, engineering sciences, social science and economics. In the this special is-sue, expository and original research papers associated with the new trends and challenges in special functions and fractional order calculus and as well as their uses in real world problems are collected. Some are invited papers. © CSP - Cambridge, UK; I&S - Florida, USA, 2021Article Citation - WoS: 19Citation - Scopus: 20Fractional Calculus Analysis of the Cosmic Microwave Background(Editura Acad Romane, 2013) Tenreiro Machado, J. A.; Baleanu, Dumitru; Stefanescu, Petruta; Tintareanu, Ovidiu; Baleanu, Dumitru; MatematikCosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.Article Citation - WoS: 5Citation - Scopus: 6Application of Sumudu and Double Sumudu Transforms To Caputo-Fractional Differential Equations(Eudoxus Press, Llc, 2012) Jarad, Fahd; Jarad, Fahd; Tas, K.; Taş, Kenan; MatematikThe definition, properties and applications of the Sumudu transform to ordinary differential equations are described in [1-3]. In this manuscript we derive the formulae for the Sumudu and double Sumudu transforms of ordinary and partial fractional derivatives and apply them in solving Caputo-fractional differential equations. Our purpose here is to show the applicability of this new transform and its efficiency in solving such problems.Book Citation - Scopus: 5Principles of Signals and Systems(Springer International Publishing, 2022) Gazi, O.The textbook presents basic concepts of signals and systems in a clear manner, based on the author's 15+ years of teaching the undergraduate course for engineering students. To attain full benefit from the content, readers should have a strong knowledge of calculus and be familiar with integration, differentiation, and summation operations. The book starts with an introduction to signals and systems and continues with coverage of basic signal functions and their manipulations; energy, power, convolution, and systems; Fourier analysis of continuous time signals and digital signals; Laplace transform; and Z transforms. Practical applications are included throughout. The book is also packed with solved examples, self-study exercises, and end of chapter problems. © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023.Article Citation - Scopus: 1On the Problem of Schoenberg On Rn(Univ Prishtines, 2024) Kushpel, Alexander; Tas, KenanIn 1946 Schoenberg introduced splines on R, which play now one of the central roles in Numerical Analysis, and posed the problem on spline interpolation. The main aim of this article is to establish explicit representations of fundamental splines on Rn and give a positive solution of the problem of Schoenberg on RnArticle 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.