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Öğe A comparative study of numerical methods for solving (n+1) dimensional and third-order partial differential equations(American Scientific Publishers, 2016) Acan, Omer; Keskin, YildirayIn this study, we compare the reduced differential transform method and the variational iteration method. This has been achieved by handling (2+1) dimensional and third-order type of the Zakharov-Kuznetsov ZK(m,m) partial differential equations. Two numerical examples have also been carried out to validate and demonstrate efficiency of the two methods. Also, it is shown that the reduced differential transform method has advantage over variational iteration method. This method is very fast, efficient, applicable and has powerful effects in linear and nonlinear problems. © 2016 American Scientific Publishers All rights reserved.Öğe A NEW NUMERICAL TECHNIQUE FOR SOLVING FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS(Univ Miskolc Inst Math, 2018) Acan, Omer; Baleanu, DumitruWe propose conformable Adomian decomposition method (CADM) for fractional partial differential equations (FPDEs). This method is a new Adomian decomposition method (ADM) based on conformable derivative operator (CDO) to solve FPDEs. At the same time, conformable reduced differential transform method (CRDTM) for FPDEs is briefly given and a numerical comparison is made between this method and the newly introduced CADM. In applied science, CADM can be used as an alternative method to obtain approximate and analytical solutions for FPDEs as CRDTM. In this study, linear and non-linear three problems are solved by these two methods. In these methods, the obtained solutions take the form of a convergent series with easily computable algorithms. For the applications, the obtained results by these methods are compared to each other and with the exact solutions. When applied to FPDEs, it is seem that CADM approach produces easy, fast and reliable solutions as CRDTM. 2010 Mathematics Subject Classification: 34A08; 34K28Öğe Analytical Approximate Solutions of (n+1)-Dimensional Fractal Heat-Like and Wave-Like Equations(Mdpi, 2017) Acan, Omer; Baleanu, Dumitru; Al Qurashi, Maysaa Mohamed; Sakar, Mehmet GiyasIn this paper, we propose a new type (n + 1)-dimensional reduced differential transform method (RDTM) based on a local fractional derivative (LFD) to solve (n + 1)-dimensional local fractional partial differential equations (PDEs) in Cantor sets. The presented method is named the (n + 1)-dimensional local fractional reduced differential transform method (LFRDTM). First the theories, their proofs and also some basic properties of this procedure are given. To understand the introduced method clearly, we apply it on the (n + 1)-dimensional fractal heat-like equations (HLEs) and wave-like equations (WLEs). The applications show that this new technique is efficient, simply applicable and has powerful effects in (n + 1)-dimensional local fractional problems.Öğe Conformable variational iteration method, conformable fractional reduced differential transform method and conformable homotopy analysis method for non-linear fractional partial differential equations(Taylor & Francis Ltd, 2020) Acan, Omer; Firat, Omer; Keskin, YildirayIn this paper, we introduce conformable variational iteration method (C-VIM), conformable fractional reduced differential transform method (CFRDTM) and conformable homotopy analysis method (C-HAM). Between these methods, the C-VIM is introduced for the first time for fractional partial differential equations (FPDEs). These methods are new versions of well-known VIM, RDTM and HAM. In addition, above-mentioned techniques are based on new defined conformable fractional derivative to solve linear and non-linear conformable FPDEs. Firstly, we present some basic definitions and general algorithm for proposal methods to solve linear and non-linear FPDEs. Secondly, to understand better, the presented new methods are supported by some examples. Finally, the obtained results are illustrated by the aid of graphics and the tables. The applications show that these new techniques C-VIM, CFRDTM and C-HAM are extremely reliable and highly accurate and it provides a significant improvement in solving linear and non-linear FPDEs.Öğe Gecikme Argümentli Rayleigh Tipi Denklem için Periyodik Çözümlerin Varlığı Üzerine(2018) Acan, OmerBu çalışmada, ? ? ? ? ? ? ? ? ? ? ? ?? ? ? ? ? ? , , 0 t f t t t g t t t t t ? ? ? ? ??? ?? ? ? ? ? ? ? ? formundaki gecikme argümentli Rayleigh tipi denklem ele alınmaktadır. Bu denklemin T-periyodik çözümlerinin varlığı üzerine yeni sonuçlar elde edilmektedir. Bu sonuçlar elde edilirken örtüşen derece teorisi kullanılmaktadır.Öğe Global existence and boundedness of solutions for a type of nonlinear integro-differential equations of third order(Balkan Society of Geometers, 2017) Ayhan, Timur; Acan, OmerIn this article, we consider a particular nonlinear integro- differential equation of the third order and discuss the continuability and boundedness of solutions of this equation. Lyapunov's second method is used in the proof of the main theorem by building an appropriate Lya- punov function. The result obtained in this paper contains and improves some well known results on the third order nonlinear integro-differential equations in literature. We also provide an example to illustrate the method. © Balkan Society of Geometers, Geometry Balkan Press 2017.Öğe New exact solution of generalized biological population model(Int Scientific Research Publications, 2017) Acan, Omer; Al Qurashi, Maysaa Mohamed; Baleanu, DumitruIn this study, a mathematical model of the generalized biological population model (GBPM) gets a new exact solution with a conformable derivative operator (CDO). The new exact solution of this model will be obtained by a new approximate analytic technique named three dimensional conformable reduced differential transform method (TCRDTM). By using this technique, it is possible to find new exact solution as well as closed analytical approximate solution of a partial differential equations (PDEs). Three numerical applications of GBPM are given to check the accuracy, effectiveness, and convergence of the TCRDTM. In these applications, obtained new exact solutions in conformable sense are compared with the exact solutions in Caputo sense in literature. The comparisons are illustrated in 3D graphics. The results show that when alpha -> 1, the exact solutions in conformable and Caputo sense converge to each other. In other cases, exact solutions different from each other are obtained. (C) 2017 All rights reserved.Öğe The Existence and Uniqueness of Periodic Solutions for A Kind of Forced Rayleigh Equation(Gazi Univ, 2016) Acan, OmerIn this study, the coincidence degree theory has been used to determine new results on the existence and uniqueness of T-periodic solutions for a type of Rayleigh equation as follows u(t) + f(t,u'))u'(t) + g(t,u(t)) = p(t).
