Browsing by Author "Golmankhaneh, Alireza K."

Now showing 1 - 20 of 48

Citation Count: Jafarian, A...et al. (2014). "A Numerical Solution of the Urysohn-Type Fredholm İntegral Equations", Romanian Journal of Physics, Vol. 59, No. 7-8, pp. 625-635.
A Numerical Solution of the Urysohn-Type Fredholm İntegral Equations
(Editura Academiei Romane, 2014) Jafarian, Ahmad; Measoomy, S. A.; Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
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 nonlinear equations is solved numerically by using the ANNs approach to yield truncated Bernstein series coefficients of the solution function. Several illustrative examples with numerical simulations are provided to support the theoretical claims.
About Maxwell's Equations On Fractal Subsets of R-3
(De Gruyter Poland SP Zoo, 2013) Golmankhaneh, Alireza K.; Golmankhaneh, Ali; Baleanu, Dumitru; 56389
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 Count: Golmankhaneh, A.K...et al. (2015). About schrodinger equation on fractals curves imbedding in R (3). International Journal of Theoretical Physics, 54(4), 1275-1282. http://dx.doi.org/10.1007/s10773-014-2325-0
About schrodinger equation on fractals curves imbedding in R (3)
(Springer/Plenum Publishers, 2015) Golmankhaneh, Alireza K.; Golmankhaneh, Ali K.; Baleanu, Dumitru
In this paper we introduced the quantum mechanics on fractal time-space. In a suggested formalism the time and space vary on Cantor-set and Von-Koch curve, respectively. Using Feynman path method in quantum mechanics and F (alpha) -calculus we find SchrA << dinger equation on on fractal time-space. The Hamiltonian and momentum fractal operator has been indicated. More, the continuity equation and the probability density is given in view of F (alpha) -calculus.
Citation Count: Jafarian, A...et al. (2020). "Analytic Solution for A Nonlinear Problem of Magneto-Thermoelasticity",Reports On Mathematical Physics, Vol. 71, No. 3.
Analytic Solution for A Nonlinear Problem of Magneto-Thermoelasticity
(2013) Jafarian, A.; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
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 Count: Jafarian, A...et al. (2014). "Analytical Approximate Solutions of the Zakharov-Kuznetsov Equations",Romanian Reports in Physics, Vol. 66, No. 2.
Analytical Approximate Solutions of the Zakharov-Kuznetsov Equations
(Editura Academiei Romane, 2014) Jafarian, Ahmad; Ghaderi, Pariya; Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
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 Count: Jafarian, A...et al. (2014). "Analytical Treatment of System of Abel Integral Equations By Homotopy Analysis Method",Romanian Reports in Physics, Vol. 66, No. 3, pp. 603-611.
Analytical Treatment of System of Abel Integral Equations By Homotopy Analysis Method
(Editura Academiei Romane, 2014) Jafarian, Ahmad; Ghaderi, Pariya; Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
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.
Citation Count: Golmankhaneh, Alireza K.; Baleanu, Dumitru (2015). "Calculus on fractals", Fractional Dynamics, pp. 307-332.
Calculus on fractals
(2015) Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
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 Count: Golmankhaneh, Alireza K.; Baleanu, Dumitru. Calculus on Fractals, in Fractional Dynamics, De Gruyter, pp. 307-332, 2015.
Calculus on Fractals
(De Gruyter, 2015) Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
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.
Citation Count: Golmankhaneh, A.K...et al. (2012). Comparison of iterative methods by solving nonlinear Sturm-Liouville, Burgers and Navier-Stokes equations. Central European Journal Of Physics, 10(4), 966-976. http://dx.doi.org/10.2478/s11534-012-0038-7
Comparison of iterative methods by solving nonlinear Sturm-Liouville, Burgers and Navier-Stokes equations
(Versita, 2012) Golmankhaneh, Alireza K.; Khatuni, Tuhid; Porghoveh, Neda A.; Baleanu, Dumitru
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 Count: Golmankhaneh, Alireza K.; Baleanu, D., "Diffraction from fractal grating Cantor sets", Journal of Modern Optics, Vol. 64, No. 14, pp. 1364-1369, (2016).
Diffraction from fractal grating Cantor sets
(Taylor&Francis LTD, 2016) Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
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 Count: Golmankhaneh, Alireza Khalili; Fernandez, Arran; Golmankhaneh, Ali Khalili; et al. (2018). Diffusion on Middle- Cantor Sets, Entropy, 20(7).
Diffusion on Middle- Cantor Sets
(MDPI, 2018) Golmankhaneh, Alireza K.; Fernandez, Arran; Baleanu, Dumitru; 56389
In this paper, we study C-calculus on generalized Cantor sets, which have self-similar properties and fractional dimensions that exceed their topological dimensions. Functions with fractal support are not differentiable or integrable in terms of standard calculus, so we must involve local fractional derivatives. We have generalized the C-calculus on the generalized Cantor sets known as middle- Cantor sets. We have suggested a calculus on the middle- Cantor sets for different values of with 0<<1. Differential equations on the middle- Cantor sets have been solved, and we have presented the results using illustrative examples. The conditions for super-, normal, and sub-diffusion on fractal sets are given.
Citation Count: Golmankhaneh, A.K., Yang, X.J., Baleanu, D. (2015). Einstein field equations within local fractional calculus. Romanian Journal of Physics, 60(1-2), 22-31.
Einstein field equations within local fractional calculus
(Editura Acad Romane, 2015) Golmankhaneh, Alireza K.; Yang, Xiao-Jun; Baleanu, Dumitru
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 Count: Golmankhaneh,A.K., Baleanu, D. (2016). Fractal calculus involving gauge function. Communications In Nonlinear Science And Numerical Simulation, 37, 125-130. http://dx.doi.org/10.1016/j.cnsns.2016.01.007
Fractal calculus involving gauge function
(Elsevier Science Bv, 2016) Golmankhaneh, Alireza K.; Baleanu, Dumitru
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
Citation Count: Baleanu, D...et al. (2009). Fractional Electromagnetic Equations Using Fractional Forms, 48(1), 3114-3123. http://dx.doi.org/10.1007/s10773-009-0109-8
Fractional Electromagnetic Equations Using Fractional Forms
(Springer/Plenum Publishers, 2009) Baleanu, Dumitru; Golmankhaneh, Ali K.; Golmankhaneh, Alireza K.; Baleanu, Mihaela Cristina
The generalized physics laws involving fractional derivatives give new models and conceptions that can be used in complex systems having memory effects. Using the fractional differential forms, the classical electromagnetic equations involving the fractional derivatives have been worked out. The fractional conservation law for the electric charge and the wave equations were derived by using this method. In addition, the fractional vector and scalar potentials and the fractional Poynting theorem have been derived
Citation Count: Baleanu, Dumitru...et.al. (2010). "Fractional mechanics on the extended phase space", Proceedings Of Asme International Design Engineering Technical Conferences And Computers And İnformation İn Engineering Conference, Vol 4, Pts A-C, pp.1025-1030.
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
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 Count: Baleanu, D., Golmankhaneh, A.K. (2009). Fractional Nambu Mechanics, 48(4), 1044-1052. http://dx.doi.org/10.1007/s10773-008-9877-9
Fractional Nambu Mechanics
(Springer/Plenum Publishers, 2009) Baleanu, Dumitru; Golmankhaneh, Alireza K.
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 Count: Baleanu, D...et al. (2010). Fractional Newtonian mechanics. Central European Journal Of Physics, 8(1), 120-125. http://dx.doi.org/10.2478/s11534-009-0085-x
Fractional Newtonian mechanics
(Versita, 2010) Baleanu, Dumitru; Golmankhaneh, Alireza K.; Nigmatullin, Raoul R.; Golmankhaneh, Ali K.
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 Count: Golmankhaneh, A.K...et al. (2011). Fractional odd-dimensional mechanics. Advance in Difference Equations. http://dx.doi.org/10.1155/2011/526472
Fractional odd-dimensional mechanics
(Springer International Publishing, 2011) Golmankhaneh, Ali K.; Golmankhaneh, Alireza K.; Baleanu, Dumitru; Baleanu, Mihaela Cristina
The classical Nambu mechanics is generalized to involve fractional derivatives using two different methods. The first method is based on the definition of fractional exterior derivative and the second one is based on extending the standard velocities to the fractional ones. Fractional Nambu mechanics may be used for nonintegrable systems with memory. Further, Lagrangian which is generate fractional Nambu equations is defined
Citation Count: Golmankhaneh, A.K...et al. (2010). Hamiltonian structure of fractional first order lagrangian. International Journal of Theoretical Physics, 49(2), 365-375. http://dx.doi.org/10.1007/s10773-009-0209-5
Hamiltonian structure of fractional first order lagrangian
(Springer/Plenum Publishers, 2010) Golmankhaneh, Ali K.; Golmankhaneh, Alireza K.; Baleanu, Dumitru; Baleanu, Mihaela Cristina
In this paper, we show that the fractional constraint Hamiltonian formulation, using Dirac brackets, leads to the same equations as those obtained from fractional Euler-Lagrange equations. Furthermore, the fractional Faddeev-Jackiw formalism was constructed
Citation Count: Golmankhaneh, Alireza K; Baleanu, Dumitru, "Heat and Maxwell's equations on cantor cubes", Romanian Reports In Physics, Vol. 69, No.2, (2017).
Heat and Maxwell's equations on cantor cubes
(Editura Academiei Romane, 2017) Golmankhaneh, Alireza K.; Baleanu, Dumitru; 56389
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.