Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 36Citation - Scopus: 41Numerical Treatment of Coupled Nonlinear Hyperbolic Klein-Gordon Equations(Editura Acad Romane, 2014) Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; Baleanu, D.; Abdelkawy, M. A.; MatematikA semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GL-C) method is proposed and developed for the numerical solution of the spatial variable for two nonlinear coupled Klein-Gordon (KG) partial differential equations. The general Jacobi-Gauss-Lobatto points are used as collocation nodes in this approach. The main characteristic behind the J-GL-C approach is that it reduces such problems to solve a system of ordinary differential equations (SODEs) in time. This system is solved by diagonally-implicit Runge-Kutta-Nystrom scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.Article Citation - WoS: 46Citation - Scopus: 48Solutions of the Fractional Davey-Stewartson Equations With Variational Iteration Method(Editura Acad Romane, 2012) Baleanu, Dumitru; Jafari, Hossain; Kadem, Abdelouahab; Yılmaz, Tuğba; Baleanu, Dumitru; Yilmaz, Tugba; Matematik; PsikolojiThis paper presents approximate analytical solutions for the fractional Davey-Stewartson equations using the Variational iteration method. The fractional derivatives are described in the Caputo sense. This method is based on the incorporation of the correction functional for the equation. The results obtained by this method have been compared with the exact solutions and show that the introduced approach is a promising tool for solving many linear and nonlinear fractional differential equations.Article Citation - WoS: 37Citation - Scopus: 38Newtonian Mechanics on Fractals Subset of Real-Line(Editura Acad Romane, 2013) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Fazlollahi, Vahideh; Baleanu, Dumitru; MatematikIn this paper, we have studied the calculus on the fractals, meanwhile Newtonian mechanics on fractals subset of real-line has been suggested. Further, work and energy theorem on fractals with the examples has been explained. Finally Langevin F-alpha-Equation on fractals is derived.Article Citation - WoS: 63Citation - Scopus: 76A Fractional Model of Convective Radial Fins With Temperature-Dependent Thermal Conductivity(Editura Acad Romane, 2017) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev; Baleanu, Dumitru; MatematikThe principal purpose of the present article is to examine a fractional model of convective radial fins having constant and temperature-dependent thermal conductivity. In order to solve fractional order energy balance equation, a numerical algorithm namely homotopy analysis transform method is considered. The fin temperature is derived in terms of thermo-geometric fin parameter. Our method is not limited to the use of a small parameter, such as in the standard perturbation technique. The numerical simulation for temperature and fin tip temperature are presented graphically. The results can be used in thermal design to consider radial fins having both constant and temperature-dependent thermal conductivity.Article Citation - WoS: 60Citation - Scopus: 68Lyapunov-Krasovskii Stability Theorem for Fractional Systems With Delay(Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, D.; Ranjbar N, A.; Abdeljawad, Thabet; Sadati R, S. J.; Delavari, R. H.; Abdeljawad (Maraaba), T.; Gejji, V.; MatematikFractional calculus techniques and methods started to be applied during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative and we extended Lyapunov-Krasovskii theorem for the fractional nonlinear systems.Article Citation - WoS: 19Citation - Scopus: 18On Fractional Coupled Whitham-Broer Equations(Editura Acad Romane, 2011) Kadem, Abdelouahab; Baleanu, Dumitru; Baleanu, Dumitru; MatematikFinding the fractional version of a given classical nonlinear equation or to a given system of differential equations is still an open problem in the field of the fractional calculus. In this paper the homotopy perturbation method is used to find an analytical approximate solution for the coupled Whitham-Broer-Kaup equations. The obtained results indicate that the method is efficient and accurate.Article Citation - WoS: 16Citation - Scopus: 23On Fractional Hamiltonian Systems Possessing First-Class Constraints Within Caputo Derivatives(Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, Dumitru; Muslih, Sami I.; Rabei, Eqab M.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; MatematikThe fractional constrained systems possessing only first class constraints are analyzed within Caputo fractional derivatives. It was proved that the fractional Hamilton-Jacobi like equations appear naturally in the process of finding the full canonical transformations. An illustrative example is analyzed.Article Citation - WoS: 34Citation - Scopus: 38On the Fractional-Order Diffusion-Wave Process(Editura Acad Romane, 2010) Herzallah, Mohamed A. E.; Baleanu, Dumitru; El-Sayed, Ahmed M. A.; Baleanu, Dumtru; MatematikOne of the main applications of the fractional calculus, integration and differentiation of arbitrary orders is the modelling of the intermediate physical processes. Here we formulate a more general model which represents the diffusion wave process in all its cases, and give some examples discussing these different cases.Article Citation - WoS: 34Citation - Scopus: 36Exact Solutions of Boussinesq and Kdv-Mkdv Equations by Fractional Sub-Equation Method(Editura Acad Romane, 2013) Jafari, Hossein; Baleanu, Dumitru; Tajadodi, Haleh; Baleanu, Dumitru; Al-Zahrani, Abdulrahim A.; Alhamed, Yahia A.; Zahid, Adnan H.; MatematikA fractional sub-equation method is introduced to solve fractional differential equations. By the aid of the solutions of the fractional Riccati equation, we construct solutions of the Boussinesq and KdV-mKdV equations of fractional order. The obtained results show that this method is very efficient and easy to apply for solving fractional partial differential equations.Article Citation - WoS: 9Citation - Scopus: 9Positivity Preserving Computational Techniques for Nonlinear Autocatalytic Chemical Reaction Model(Editura Acad Romane, 2020) Ahmed, Nauman; Baleanu, Dumitru; Baleanu, Dumitru; Korkmaz, Alper; Rafiq, Muhammad; Rehman, Muhammad Aziz-Ur; Ali, Mubasher; MatematikIn many physical problems, positivity is one of the most prevalent and imperative attribute of diverse mathematical models such as concentration of chemical reactions, population dynamics etc. However, the numerical discretization of dynamical systems that illustrate negative values may lead to meaningless solutions and sometimes to their divergence. The main objective of this work is to develop positivity preserving numerical schemes for the two-dimensional autocatalytic reaction diffusion Brusselator model. Two explicit finite difference (FD) schemes are proposed to solve numerically the two-dimensional Brusselator system. The proposed methods are the non-standard finite difference (NSFD) scheme and the unconditionally positivity preserving scheme. These numerical methods retain the positivity of the solution and the stability of the equilibrium point. Both proposed numerical schemes are compared with the forward Euler explicit FD scheme. The stability and consistency of all schemes are proved analytically and then verified by numerical simulations.