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He, Ji-Huan

Comment on “Variational iteration method for fractional calculus using He’s polynomials”. (English) Zbl 1256.65091

Abstr. Appl. Anal. 2012, Article ID 964974, 2 p. (2012).
Summary: Recently, Y. Liu [ibid. 2012, Article ID 727031, 10 p. (2012; Zbl 1246.65191)] applied the variational homotopy perturbation method for fractional initial boundary value problems. This note concludes that the method is a modified variational iteration method using He’s polynomials. A standard variational iteration algorithm for fractional differential equations is suggested.

Cited in 4 Documents

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Citations:

Zbl 1246.65191
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\textit{J.-H. He}, Abstr. Appl. Anal. 2012, Article ID 964974, 2 p. (2012; Zbl 1256.65091)
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References:

[1] J.-H. He, “Some asymptotic methods for strongly nonlinear equations,” International Journal of Modern Physics B, vol. 20, no. 10, pp. 1141-1199, 2006. · Zbl 1102.34039
[2] J.-H. He, “Approximate analytical solution for seepage flow with fractional derivatives in porous media,” Computer Methods in Applied Mechanics and Engineering, vol. 167, no. 1-2, pp. 57-68, 1998. · Zbl 0942.76077
[3] Y. Liu, “Variational homotopy perturbation method for solving fractional initial boundary value problems,” Abstract and Applied Analysis, vol. 2012, Article ID 727031, 10 pages, 2012. · Zbl 1246.65191
[4] J. H. He, “Asymptotic methods for solitary solutions and compactons,” Abstract and Applied Analysis, vol. 2012, Article ID 916793, 130 pages, 2012. · Zbl 1257.35158
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[8] M. A. Noor and S. T. Mohyud-Din, “Variational iteration method for fifth-order boundary value problems using He’s polynomials,” Mathematical Problems in Engineering, vol. 2008, Article ID 954794, 12 pages, 2008. · Zbl 1151.65334
[9] S. Guo and L. Mei, “The fractional variational iteration method using He’s polynomials,” Physics Letters A, vol. 375, no. 3, pp. 309-313, 2011. · Zbl 1241.35216
[10] J. Ji, J. Zhang, and Y. Dong, “The fractional variational iteration method improved with the Adomian series,” Applied Mathematics Letters, vol. 25, no. 12, pp. 2223-2226, 2012. · Zbl 1252.65115
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