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

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Golmankhaneh A., Khatuni T., Porghoveh N., Baleanu D.
Open Physics
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2012
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vol. 10
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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.
2
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Fractional Newtonian mechanics

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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.
3
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About Maxwell’s equations on fractal subsets of ℝ3

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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.
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