WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
Browse
58 results
Search Results
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: 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: 20Citation - Scopus: 27Solving Partial Q-Differential Equations Within Reduced Q-Differential Transformation Method(Editura Acad Romane, 2014) Jafari, H.; Baleanu, Dumitru; Haghbin, A.; Hesam, S.; Baleanu, D.; MatematikIn this paper, the reduced q-differential transform method is presented for solving partial differential equations. In this method, the solution is calculated in the form of convergent power series with easily computable components. Three test problems are discussed to illustrate the effectiveness and performance of the proposed method. The results show that the proposed iteration technique is very effective and convenient.Article Citation - WoS: 13Citation - Scopus: 16Generalized Laguerre-Gauss Scheme for First Order Hyperbolic Equations on Semi-Infinite Domains(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Hafez, R. M.; Alzahrani, E. O.; Baleanu, D.; Alzahrani, A. A.; MatematikIn this article, we develop a numerical approximation for first-order hyperbolic equations on semi-infinite domains by using a spectral collocation scheme. First, we propose the generalized Laguerre-Gauss-Radau collocation scheme for both spatial and temporal discretizations. This in turn reduces the problem to the obtaining of a system of algebraic equations. Second, we use a Newton iteration technique to solve it. Finally, the obtained results are compared with the exact solutions, highlighting the performance of the proposed numerical method.Article Citation - WoS: 1Citation - Scopus: 2Motion of a Spherical Particle in a Rotating Parabola Using Fractional Lagrangian(Univ Politehnica Bucharest, Sci Bull, 2017) Baleanu, D.; Baleanu, Dumitru; Asad, J. H.; Alipour, M.; Blaszczyk, T.; MatematikIn this work, the fractional Lagrangian of a particle moving in a rotating parabola is used to obtain the fractional Euler- Lagrange equations of motion where derivatives within it are given in Caputo fractional derivative. The obtained fractional Euler- Lagrange equations are solved numerically by applying the Bernstein operational matrices with Tau method. The results obtained are very good and when the order of derivative closes to 1, they are in good agreement with those obtained in Ref. [10] using Multi step- Differential Transformation Method (Ms-DTM).Article Citation - WoS: 15Citation - Scopus: 10Einstein Field Equations Within Local Fractional Calculus(Editura Acad Romane, 2015) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Yang, Xiao-Jun; Baleanu, D.; MatematikIn this paper, we introduce the local fractional Christoffel index symbols of the first and second kind. The divergence of a local fractional contravariant vector and the curl of local fractional covariant vector are defined. The fractional intrinsic derivative is given. The local fractional Riemann-Christoffel and Ricci tensors are obtained. Finally, the Einstein tensor and Einstein field are generalized by involving the fractional derivatives. Illustrative examples are presented.Article Citation - WoS: 29Citation - Scopus: 31A Novel Spectral Approximation for the Two-Dimensional Fractional Sub-Diffusion Problems(Editura Acad Romane, 2015) Bhrawy, A. H.; Baleanu, Dumitru; Zaky, M. A.; Baleanu, D.; Abdelkawy, M. A.; MatematikThis paper reports a new numerical method that enables easy and convenient discretization of a two-dimensional sub-diffusion equation with fractional derivatives of any order. The suggested method is based on Jacobi tau spectral procedure together with the Jacobi operational matrix for fractional derivatives, described in the Caputo sense. Such approach has the advantage of reducing the problem to the solution of a system of algebraic equations, which may then be solved by any standard numerical technique. The validity and effectiveness of the method are demonstrated by solving two numerical examples, which are presented in the form of tables and graphs to make more easier comparisons with the exact solutions and the results obtained by other methods.Article Citation - WoS: 26Citation - Scopus: 25Numerical Investigations on the Physical Dynamics of the Coupled Fractional Boussinesq-Burgers System(Editura Acad Romane, 2020) Abu Irwaq, I.; Baleanu, Dumitru; Alquran, M.; Jaradat, I; Noorani, M. S. M.; Momani, S.; Baleanu, D.; MatematikThe coupled Boussinesq-Burgers system is a physical model of fluid flows in a dynamical system that describes the propagation of shallow water waves. In this work, we upgrade this model to include time-fractional derivatives. The effect of the fractional order in the propagation of the obtained solutions is discussed by using an adaptation of both the time-spectrum function method and the homotopy perturbation method. One of the main findings worth to be mentioned, is that the field functions involved in the coupled fractional Boussinesq-Burgers system have different stability behaviors. Tables and 3D plots regarding the accuracy of the proposed numerical methods are presented and comparison is made to show the preference of either method.Article Citation - WoS: 52Citation - Scopus: 54Fractional Caputo Heat Equation Within the Double Laplace Transform(Editura Acad Romane, 2013) Jarad, Fahd; Anwar, A. M. O.; Jarad, Fahd; Baleanu, Dumitru; Baleanu, D.; Ayaz, F.; MatematikThe heat equation and its fractional generalization are used in various applications in science and engineering. In this paper firstly we introduce the double Laplace transform of the partial fractional integrals and derivatives which can be used to solve partial differential equations with Caputo fractional derivatives. Secondly, the fractional heat equation was investigated in details with the help of this new generalized transformArticle Citation - WoS: 19The First Integral Method for The (3+1)-Dimensional Modified Korteweg-De Vries-Zakharov and Hirota Equations(Editura Acad Romane, 2015) Baleanu, D.; Baleanu, Dumitru; Killic, B.; Ugurlu, Y.; Inc, M.; MatematikThe first integral method is applied to get the different types of solutions of the (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov and Hirota equations. We obtain envelope, bell shaped, trigonometric, and kink soliton solutions of these nonlinear evolution equations. The applied method is an effective one to obtain different types of solutions of nonlinear partial differential equations.