Browsing by Author "Golmankhaneh, Ali K."

Now showing 1 - 12 of 12

Citation - WoS: 19
Citation - Scopus: 21
About Maxwell's Equations on Fractal Subsets of R³
(de Gruyter Poland Sp Z O O, 2013) Golmankhaneh, Ali K.; Baleanu, Dumitru; Golmankhaneh, Alireza K.
In this paper we have generalized -calculus for fractals embedding in a"e(3). -calculus is a fractional local derivative on fractals. It is an algorithm which may be used for computer programs and is more applicable than using measure theory. In this Calculus staircase functions for fractals has important role. -fractional differential form is introduced such that it can help us to derive the physical equation. Furthermore, using the -fractional differential form of Maxwell's equations on fractals has been suggested.
Fractional mechanics on the extended phase space
(Amer Soc Mechanical Engineers, 2010) Baleanu, Dumitru; Muslih, Sami I.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Rabei, Eqab M.
Fractional calculus has gained a lot of importance and potential applications in several areas of science and engineering. The fractional dynamics and the fractional variational principles started to be used intensively as an alternative tool in order to describe the physical complex phenomena. In this paper we have discussed the fractional extension of the classical dynamics. The fractional Hamiltonian is constructed and the fractional generalized Poisson's brackets on the extended phase space is established.
Citation - WoS: 24
Citation - Scopus: 33
Fractional Nambu Mechanics
(Springer/plenum Publishers, 2009) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, Dumitru
The fractional generalization of Nambu mechanics is constructed by using the differential forms and exterior derivatives of fractional orders. The generalized Pfaffian equations are obtained and one example is investigated in details.
Citation - WoS: 62
Citation - Scopus: 70
Fractional Newtonian Mechanics
(de Gruyter Poland Sp Z O O, 2010) Golmankhaneh, Alireza K.; Nigmatullin, Raoul; Golmankhaneh, Ali K.; Baleanu, Dumitru
In the present paper, we have introduced the generalized Newtonian law and fractional Langevin equation. We have derived potentials corresponding to different kinds of forces involving both the right and the left fractional derivatives. Illustrative examples have worked out to explain the formalism.
Citation - WoS: 41
Citation - Scopus: 41
Homotopy 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; Matematik
Numerical 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.
Citation - WoS: 65
Citation - Scopus: 72
Newtonian Law With Memory
(Springer, 2010) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Nigmatullin, Raoul R.; Baleanu, Dumitru
In this study we analyzed the Newtonian equation with memory. One physical model possessing memory effect is analyzed in detail. The fractional generalization of this model is investigated and the exact solutions within Caputo and Riemann-Liouville fractional derivatives are reported.
Citation - WoS: 87
Citation - Scopus: 96
On Electromagnetic Field in Fractional Space
(Pergamon-elsevier Science Ltd, 2010) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, Dumitru
Laplacian equation in fractional space describes complex phenomena of physics. With this view, potential of charge distribution in fractional space is derived using Gegenbauer polynomials. Multipoles and magnetic field of charges in fractional space have been obtained. (C) 2008 Elsevier Ltd. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 3
On Fractional Dynamics on the Extended Phase Space
(Asme, 2010) Muslih, Sami I.; Rabei, Eqab M.; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, Dumitru
Fractional calculus should be applied to various dynamical systems in order to be validated in practice. On this line of taught, the fractional extension of the classical dynamics is introduced. The fractional Hamiltonian on the extended phase space is analyzed and the corresponding generalized Poisson's brackets are constructed. [DOI: 10.1115/1.4002091]
Citation - WoS: 16
Citation - Scopus: 23
On 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.; Matematik
The 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.
On nonlinear fractional Klein-Gordon equation
(Elsevier Science Bv, 2011) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, Dumitru
Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Cordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order a are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equation
Citation - WoS: 125
Citation - Scopus: 136
On Nonlinear Fractional Klein-Gordon Equation
(Elsevier, 2011) Golmankhaneh, Ali K.; Baleanu, Dumitru; Golmankhaneh, Alireza K.
Numerical methods are used to find exact solution for the nonlinear differential equations. In the last decades Iterative methods have been used for solving fractional differential equations. In this paper, the Homotopy perturbation method has been successively applied for finding approximate analytical solutions of the fractional nonlinear Klein-Cordon equation can be used as numerical algorithm. The behavior of solutions and the effects of different values of fractional order a are shown graphically. Some examples are given to show ability of the method for solving the fractional nonlinear equation. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.
Citation - WoS: 26
Citation - Scopus: 32
Solving 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.; Matematik
In 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.