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1
Content available remote

Cosmological perturbations in FRW model with scalar field within Hamilton-Jacobi formalism and symplectic projector method

100%
Baleanu D.
Open Physics
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2006
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vol. 4
|
issue 4
503-510
EN
The Hamilton-Jacobi analysis is applied to the dynamics of the scalar fluctuations about the Friedmann-Robertson-Walker (FRW) metric. The gauge conditions are determined from the consistency conditions. The physical degrees of freedom of the model are obtained by the symplectic projector method. The role of the linearly dependent Hamiltonians and the gauge variables in the Hamilton-Jacobi formalism is discussed.
2
Content available remote

Constant curvature coefficients and exact solutions in fractional gravity and geometric mechanics

64%
Baleanu D., Vacaru S.
Open Physics
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2011
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vol. 9
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issue 5
1267-1279
EN
We present a study of fractional configurations in gravity theories and Lagrange mechanics. The approach is based on a Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists of a proof that, for corresponding classes of nonholonomic distributions, a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.
3
Content available remote

Gravitational potential in fractional space

51%
Muslih S., Baleanu D., Rabei E.
Open Physics
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2007
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vol. 5
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issue 3
285-292
EN
In this paper the gravitational potential with β-th order fractional mass distribution was obtained in α dimensionally fractional space. We show that the fractional gravitational universal constant G α is given by $$G_\alpha = \frac{{2\Gamma \left( {\frac{\alpha }{2}} \right)}}{{\pi ^{\alpha /2 - 1} (\alpha - 2)}}G$$ , where G is the usual gravitational universal constant and the dimensionality of the space is α > 2.
4
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About Maxwell’s equations on fractal subsets of ℝ3

51%
Golmankhaneh A., Golmankhaneh A., Baleanu D.
Open Physics
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2013
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vol. 11
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issue 6
863-867
EN
In this paper we have generalized $$F^{\bar \xi }$$-calculus for fractals embedding in ℝ3. $$F^{\bar \xi }$$-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. $$F^{\bar \xi }$$-fractional differential form is introduced such that it can help us to derive the physical equation. Furthermore, using the $$F^{\bar \xi }$$-fractional differential form of Maxwell’s equations on fractals has been suggested.
5
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Fractional Hamilton’s equations of motion in fractional time

51%
Muslih S., Baleanu D., Rabei E.
Open Physics
|
2007
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vol. 5
|
issue 4
549-557
EN
The Hamiltonian formulation for mechanical systems containing Riemman-Liouville fractional derivatives are investigated in fractional time. The fractional Hamilton’s equations are obtained and two examples are investigated in detail.
6
Content available remote

Fractional order modelling of zero length column desorption response for adsorbents with variable particle sizes

51%
Machado J., Zaman S., Baleanu D.
Open Physics
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2013
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vol. 11
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issue 6
881-885
EN
This manuscript analyses the data generated by a Zero Length Column (ZLC) diffusion experimental set-up, for 1,3 Di-isopropyl benzene in a 100% alumina matrix with variable particle size. The time evolution of the phenomena resembles those of fractional order systems, namely those with a fast initial transient followed by long and slow tails. The experimental measurements are best fitted with the Harris model revealing a power law behavior.
7
Content available remote

Travelling wave solutions: A new approach to the analysis of nonlinear physical phenomena

51%
Sayevand K., Baleanu D., Fardi M.
Open Physics
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2014
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vol. 12
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issue 7
480-489
EN
In this manuscript, a reliable scheme based on a general functional transformation is applied to construct the exact travelling wave solution for nonlinear differential equations. Our methodology is investigated by means of the modified homotopy analysis method which contains two convergence-control parameters. The obtained results reveal that the proposed approach is a very effective. Several illustrative examples are investigated in detail.
8
Content available remote

Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter

51%
Delavari H., Senejohnny D., Baleanu D.
Open Physics
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2012
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vol. 10
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issue 5
1095-1101
EN
In this paper, we propose an observer-based fractional order chaotic synchronization scheme. Our method concerns fractional order chaotic systems in Brunovsky canonical form. Using sliding mode theory, we achieve synchronization of fractional order response with fractional order drive system using a classical Lyapunov function, and also by fractional order differentiation and integration, i.e. differintegration formulas, state synchronization proved to be established in a finite time. To demonstrate the efficiency of the proposed scheme, fractional order version of a well-known chaotic system; Arnodo-Coullet system is considered as illustrative examples.
9
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Fractional Newtonian mechanics

51%
Baleanu D., Golmankhaneh A., Nigmatullin R., Golmankhaneh A.
Open Physics
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2010
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vol. 8
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issue 1
120-125
EN
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.
10
Content available remote

The variational iteration method for solving n-th order fuzzy differential equations

51%
Jafari H., Saeidy M., Baleanu D.
Open Physics
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2012
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vol. 10
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issue 1
76-85
EN
The variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.
11
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Variational iteration method - a promising technique for constructing equivalent integral equations of fractional order

51%
Wang Y.-H., Wu G.-C., Baleanu D.
Open Physics
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2013
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vol. 11
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issue 10
1392-1398
EN
The variational iteration method is newly used to construct various integral equations of fractional order. Some iterative schemes are proposed which fully use the method and the predictor-corrector approach. The fractional Bagley-Torvik equation is then illustrated as an example of multi-order and the results show the efficiency of the variational iteration method’s new role.
12
Content available remote

Homotopy analysis method for solving Abel differential equation of fractional order

51%
Jafari H., Sayevand K., Tajadodi H., Baleanu D.
Open Physics
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2013
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vol. 11
|
issue 10
1523-1527
EN
In this study, the homotopy analysis method is used for solving the Abel differential equation with fractional order within the Caputo sense. Stabilityand convergence of the proposed approach is investigated. The numerical results demonstrate that the homotopy analysis method is accurate and readily implemented.
13
Content available remote

Comparison of iterative methods by solving nonlinear Sturm-Liouville, Burgers and Navier-Stokes equations

51%
Golmankhaneh A., Khatuni T., Porghoveh N., Baleanu D.
Open Physics
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2012
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vol. 10
|
issue 4
966-976
EN
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.
14
Content available remote

On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials

45%
Babolian E., Hamedzadeh D., Jafari H., Hajikandi A. A., Baleanu D.
Open Physics
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2015
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vol. 13
|
issue 1
EN
This paper is concerned with the numerical solution for a class of weakly singular Fredholm integral equations of the second kind. The Taylor series of the unknown function, is used to remove the singularity and the truncated Taylor series to second order of k(x, y) about the point (x0, y0) is used. The integrals that appear in this method are computed exactly and some of these integrals are computed with the Cauchy principal value without using numerical quadratures. The solution in the Legendre polynomial form generates a system of linear algebraic equations, this system is solved numerically. Through numerical examples, performance of the present method is discussed concerning the accuracy of the method.
15
Content available remote

Fractional sub-equation method for the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation

39%
Jafari H., Tajadodi H., Baleanu D., Al-Zahrani A., Alhamed Y., Zahid A.
Open Physics
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2013
|
vol. 11
|
issue 10
1482-1486
EN
In this paper the fractional sub-equation method is used to construct exact solutions of the fractional generalized reaction Duffing model and nonlinear fractional Sharma-Tasso-Olver equation.The fractional derivative is described in the Jumarie’s modified Riemann-Liouville sense. Two illustrative examples are given, showing the accuracy and convenience of the method.
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