Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 20Citation - Scopus: 24Optimal System, Nonlinear Self-Adjointness and Conservation Laws for Generalized Shallow Water Wave Equation(de Gruyter Poland Sp Zoo, 2018) Inc, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, DumitruIn this article, the generalized shallow water wave (GSWW) equation is studied from the perspective of one dimensional optimal systems and their conservation laws (Cls). Some reduction and a new exact solution are obtained from known solutions to one dimensional optimal systems. Some of the solutions obtained involve expressions with Bessel function and Airy function [1-3]. The GSWW is a nonlinear self-adjoint (NSA) with the suitable differential substitution, Cls are constructed using the new conservation theorem.Article Citation - WoS: 9Citation - Scopus: 11Sturm-Liouville Difference Equations Having Bessel and Hydrogen Atom Potential Type(de Gruyter Poland Sp Zoo, 2018) Ozarslan, Ramazan; Baleanu, Dumitru; Bas, ErdalIn this work, we bring a different approach for Sturm-Liouville problems having Bessel and hydrogen atom type and we provide a basis for direct and inverse problems. From this point of view, we find representations of solutions and asymptotic expansions for eigenfunctions. Furthermore, some numerical estimations are given to illustrate the necessity of the Sturm-Liouville difference equations with the potential function for the convenience to the spectral theory. The behavior of eigenfunctions for the Sturm-Liouville problem having Bessel and hydrogen atom potential type is analyzed and compared to each other. And then, comparisons are showed by tables and figures.Article Citation - WoS: 38Citation - Scopus: 44New Analytical Solutions for Conformable Fractional Pdes Arising in Mathematical Physics by Exp-Function Method(de Gruyter Poland Sp Zoo, 2017) Cenesiz, Yucel; Kurt, Ali; Baleanu, Dumitru; Tasbozan, OrkunModelling of physical systems mathematically, produces nonlinear evolution equations. Most of the physical systems in nature are intrinsically nonlinear, therefore modelling such systems mathematically leads us to nonlinear evolution equations. The analysis of the wave solutions corresponding to the nonlinear partial differential equations (NPDEs), has a vital role for studying the nonlinear physical events. This article is written with the intention of finding the wave solutions of Nizhnik-Novikov-Veselov and Klein-Gordon equations. For this purpose, the exp-function method, which is based on a series of exponential functions, is employed as a tool. This method is an useful and suitable tool to obtain the analytical solutions of a considerable number of nonlinear FDEs within a conformable derivative.Article Citation - WoS: 6Citation - Scopus: 8Application of Anns Approach for Wave-Like and Heat-Like Equations(de Gruyter Poland Sp Zoo, 2017) Baleanu, Dumitru; Jafarian, AhmadArtificial neural networks are data processing systems which originate from human brain tissue studies. The remarkable abilities of these networks help us to derive desired results from complicated raw data. In this study, we intend to duplicate an efficient iterative method to the numerical solution of two famous partial differential equations, namely the wave-like and heat-like problems. It should be noted that many physical phenomena such as coupling currents in a flat multi-strand two-layer super conducting cable, non-homogeneous elastic waves in soils and earthquake stresses, are described by initial-boundary value wave and heat partial differential equations with variable coefficients. To the numerical solution of these equations, a combination of the power series method and artificial neural networks approach, is used to seek an appropriate bivariate polynomial solution of the mentioned initial-boundary value problem. Finally, several computer simulations confirmed the theoretical results and demonstrating applicability of the method.