WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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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: 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: 20Citation - Scopus: 21Analytical Approximate Solutions of the Zakharov-Kuznetsov Equations(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; MatematikIn this paper, analytical approximate solutions for the Zakharov-Kuznetsov equations by homotopy analysis method (HAM) and the He's polynomials iterative method (HPIM) are presented. Our results indicate the remarkable efficiency of HAM as compared to HPIM. The convergence of these two methods is also analyzed.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: 11Citation - Scopus: 15Heat and Maxwell's Equations on Cantor Cubes(Editura Acad Romane, 2017) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Baleanu, Dumitru; MatematikThe fractal physics is an important research domain due to its scaling properties that can be seen everywhere in the nature. In this work, the generalized Maxwell's equations are given using fractal differential equations on the Cantor cubes and the electric field for the fractal charge distribution is derived. Moreover, the fractal heat equation is defined, which can be an adequate mathematical model for describing the flowing of the heat energy in fractal media. The suggested models are solved and the plots of the corresponding solutions are presented. A few illustrative examples are given to demonstrate the application of the obtained results in solving diverse physical problems.Article Citation - WoS: 41Citation - Scopus: 41Homotopy Perturbation Method for Solving a System of Schrodinger-Korteweg Vries Equations(Editura Acad Romane, 2011) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Golmankhaneh, Ali K.; Baleanu, Dumitru; MatematikNumerical methods used to find exact solution for the nonlinear differential equations. During the past decades Iterative methods has attracted attention of researcher for solving fractional differential equations. In the present paper, the homotopy perturbation method has been successively used to obtain approximate analytical solutions of the fractional coupled Schrodinger-Korteweg-de Vries and coupled system of diffusion-reaction equation equations. We consider fractional derivative in the Caputo sense. We have illustrated by examples the ability of proposed algorithm for solving fractional system of nonlinear equation.Article Citation - WoS: 3Citation - Scopus: 7A Numerical Solution of the Urysohn-Type Fredholm Integral Equations(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Measoomy, S. A.; Golmankhaneh, Alireza K.; Baleanu, D.; MatematikIn the present paper, a combination of the Bernstein polynomials and artificial neural networks (ANNs) is presented for solving the non-linear Urysohn equation. These polynomials are utilized to reduce the solution of the given problem to the solution of a system of non-linear algebraic equations. The remaining set of non-linear equations is solved numerically by using the ANNs approach to yield truncated Bernstein series coefficients a the solution function. Several illustrative examples with numerical simulations are provided to support the theoretical claims.Article Citation - WoS: 26Citation - Scopus: 32Solving of the Fractional Non-Linear and Linear Schrodinger Equations by Homotopy Perturbation Method(Editura Acad Romane, 2009) Baleanu, Dumitru; Baleanu, Dumitru; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; MatematikIn this paper, the homotopy perturbation method is applied to obtain approximate analytical solutions of the fractional non-linear Schrodinger equations. The solutions are obtained in the form of rapidly convergent infinite series with easily computable terms. We illustrated the ability of the method for solving fractional non linear equation by some examples.Article Citation - WoS: 48Citation - Scopus: 53Mean Square Solutions of Second-Order Random Differential Equations by Using Homotopy Analysis Method(Editura Acad Romane, 2013) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Porghoveh, Neda A.; Baleanu, D.; MatematikIn this paper, the Homotopy Analysis Method (HAM) is successfully applied for solving second-order random differential equations, homogeneous or inhomogeneous. Expectation and variance of the approximate solutions are computed. Several numerical examples are presented to show the ability and efficiency of this method.Article Citation - WoS: 20Citation - Scopus: 22Analytical Treatment of System of Abel Integral Equations by Homotopy Analysis Method(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; MatematikAbel equation has important applications in describing the least time for an object which is sliding on surface without friction in uniform gravity, and the classical theory of elasticity of materials is modeled by a system of Abel integral equations. In this manuscript, the homotopy analysis method is presented for obtaining analytical solutions of a system of Abel integral equations as fractional equations. The applied method has lessened the size of calculation and improved the accuracy of solution in the case of the singular Abel integral equation. The illustrated examples and numerical results have proved the assertion.