Browsing by Author "Golmankhaneh, Alireza K."

Now showing 1 - 20 of 35

Citation - WoS: 3
Citation - Scopus: 6
A Numerical Solution of the Urysohn-Type Fredholm İntegral Equations
(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Measoomy, S. A.; Golmankhaneh, Alireza K.; Baleanu, D.; 56389; Matematik
In 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.
Citation - WoS: 19
Citation - Scopus: 21
About Maxwell's Equations On Fractal Subsets of R-3
(de Gruyter Poland Sp Z O O, 2013) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Golmankhaneh, Ali K.; Baleanu, Dumitru; 56389; Matematik
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.
Citation - WoS: 5
Citation - Scopus: 6
Analytic Solution for A Nonlinear Problem of Magneto-Thermoelasticity
(Pergamon-elsevier Science Ltd, 2013) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; 56389; Matematik
In this paper, we present a comparative study of the homotopy analysis method (HAM), the variational iteration method (VIM) and the iterative method (He's polynomials). The approximate solution of the coupled harmonic waves nonlinear magneto-thermoelasticity equations under influence of rotation is obtained. In order to control and adjust the convergence region and the rate of solution series, we show that it is possible to choose a valid auxiliary parameter h of HAM. Using the boundary and the initial conditions we select a suitable initial approximation. The results show that these methods are very efficient, convenient and applicable to a large class of problems.
Citation - WoS: 20
Citation - Scopus: 21
Analytical Approximate Solutions of the Zakharov-Kuznetsov Equations
(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; 56389; Matematik
In 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.
Citation - WoS: 20
Citation - Scopus: 22
Analytical 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.; 56389; Matematik
Abel 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.
Calculus on Fractals
(De Gruyter, 2015) Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
In this chapter we present a framework and a calculus on fractals. The sug-gested equation has been solved and applied in physics and dynamics.
Calculus on fractals
(2015) Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
In this chapter we present a framework and a calculus on fractals. The suggested equation has been solved and applied in physics and dynamics.
Citation - WoS: 31
Citation - Scopus: 30
Comparison of iterative methods by solving nonlinear Sturm-Liouville, Burgers and Navier-Stokes equations
(de Gruyter Poland Sp Z O O, 2012) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Khatuni, Tuhid; Porghoveh, Neda A.; Baleanu, Dumitru; Matematik
In this manuscript the homotopy perturbation method, the new iterative method, and the variational iterative method have been successively used to obtain approximate analytical solutions of nonlinear Sturm-Liouville, Navier-Stokes and Burgers' equations. It is shown that the homotopy perturbation method gives approximate analytical solution near to the exact one. We have illustrated the obtained results by sketching the graph of the solutions.
Citation - WoS: 23
Citation - Scopus: 29
Diffraction from fractal grating Cantor sets
(Taylor & Francis Ltd, 2016) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Baleanu, D.; 56389; Matematik
In this paper, we have generalized the Fa-calculus by suggesting Fourier and Laplace transformations of the function with support of the fractals set which are the subset of the real line. Using this generalization, we have found the diffraction fringes from the fractal grating Cantor sets.
Citation - WoS: 14
Citation - Scopus: 8
Einstein field equations within local fractional calculus
(Editura Acad Romane, 2015) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Yang, Xiao-Jun; Baleanu, D.; Matematik
In 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.
Citation - WoS: 31
Citation - Scopus: 33
Fractal calculus involving gauge function
(Elsevier, 2016) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
Henstock-Kurzweil integral or gauge integral is the generalization of the Riemann integral. The functions which are not integrable because of singularity in the senses of Lebesgue or Riemann are gauge integrable. In this manuscript, we have generalized F-alpha-calculus using the gauge integral method for the integrating of the functions on fractal set subset of real-line where they have singularities. The suggested new method leads to the wider class of functions on the fractal subset of real-line that are *F-alpha-integrable, Using gauge function we define *F-alpha-derivative of functions their *F-alpha-derivative is not exist. The reported results can be used for generalizing the fundamental theorem of F-alpha-calculus. (C) 2016 Elsevier B.V. All rights reserved.
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.; 56389; Matematik
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: 0
Citation - Scopus: 0
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.; Matematik
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: 32
Fractional Nambu Mechanics
(Springer/plenum Publishers, 2009) Baleanu, Dumitru; Baleanu, Dumitru; Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Matematik
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: 69
Fractional Newtonian mechanics
(de Gruyter Poland Sp Z O O, 2010) Baleanu, Dumitru; Baleanu, Dumitru; Golmankhaneh, Alireza K.; Nigmatullin, Raoul; Golmankhaneh, Ali K.; Matematik
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: 11
Citation - Scopus: 15
Heat and Maxwell's equations on cantor cubes
(Editura Acad Romane, 2017) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
The 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.
Heat and Maxwell’s equations on cantor cubes
(2017) Baleanu, Dumitru; Baleanu, Dumitru; 56389; Matematik
The 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. © 2017, Editura Academiei Romane. All rights reserved.
Citation - WoS: 20
Homotopy analysis method for solving coupled Ramani equations
(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; 56389; Matematik
In this manuscript, coupled Ramani equations are solved by means of an analytic technique, namely the homotopy analysis method (HAM). The HAM is a capable and a straightforward analytic tool for solving nonlinear problems and does not need small parameters in the governing equations and boundary/initial conditions. The result of this study presents the utility and sufficiency of HAM method. Comparisons demonstrate that there is a good agreement between the HAM solutions and the exact solutions.
Citation - WoS: 40
Citation - Scopus: 40
Homotopy Perturbation Method for Solving A System of Schrodinger-Korteweg-De Vries Equations
(Editura Acad Romane, 2011) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Golmankhaneh, Ali K.; Baleanu, Dumitru; 56389; 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: 48
Citation - Scopus: 51
Mean Square Solutions of Second-Order Random Differential Equatıons By Using Homotopy Analysis Method
(Editura Acad Romane, 2013) Golmankhaneh, Alireza K.; Baleanu, Dumitru; Porghoveh, Neda A.; Baleanu, D.; 56389; Matematik
In 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.