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A short remark on fractional variational iteration method. (English) Zbl 1252.49027

Summary: This Letter compares the classical variational iteration method with the fractional variational iteration method. The fractional complex transform is introduced to convert a fractional differential equation to its differential partner, so that its variational iteration algorithm can be simply constructed.

MSC:

49K05 Optimality conditions for free problems in one independent variable
49S05 Variational principles of physics
26A33 Fractional derivatives and integrals
26A18 Iteration of real functions in one variable
Full Text: DOI

References:

[1] He, J. H., Int. J. Non-Linear Mech., 34, 699 (1999) · Zbl 1342.34005
[2] He, J. H., J. Comput. Appl. Math., 207, 3 (2007) · Zbl 1119.65049
[3] He, J. H.; Wu, X. H., Comput. Math. Applicat., 54, 881 (2007) · Zbl 1141.65372
[4] He, J. H., Non-perturbative Methods for Strongly Nonlinear Problems (2006), Verlag im Internet GmbH: Verlag im Internet GmbH Berlin
[5] He, J. H., Int. J. Mod. Phys. B, 20, 1141 (2006) · Zbl 1102.34039
[6] He, J. H., Int. J. Mod. Phys. B, 22, 3487 (2008)
[7] He, J. H., Comput. Meth. Appl. Mech. Eng., 167, 57 (1998) · Zbl 0942.76077
[8] He, J. H.; Wu, G. C.; Austin, F., Nonlinear Sci. Lett. A, 1, 1 (2010)
[9] Momani, S.; Odibat, Z., Chaos Solitons Fractals, 31, 1248 (2007) · Zbl 1137.65450
[10] Momani, S.; Odibat, Z., Int. J. Nonlinear Sci. Num., 7, 27 (2006) · Zbl 1401.65087
[11] Momani, S.; Odibat, Z., Phys. Lett. A, 355, 271 (2006) · Zbl 1378.76084
[12] Draganescu, G. E., J. Math. Phys., 47, 082902 (2006) · Zbl 1112.74009
[13] Ganji, D. D.; Hashemi Kachapi, Seyed H., Analysis of Nonlinear Equations in Fluids, Progress in Nonlinear Science, vol. 2 (2011), pp. 1-293
[14] Ganji, D. D.; Hashemi Kachapi, Seyed H., Analytical and Numerical Methods in Engineering and Applied Sciences, Progress in Nonlinear Science, vol. 3 (2011), pp. 1-579
[15] Wu, G.; Lee, E. W.M., Phys. Lett. A, 374, 2506 (2010) · Zbl 1237.34007
[16] Guo, S.; Mei, L., Phys. Lett. A, 375, 309 (2011) · Zbl 1241.35216
[17] Wu, G. C., Comput. Math. Applicat., 61, 2186 (2011) · Zbl 1219.65085
[18] Li, Z. B.; He, J. H., Math. Comput. Applicat., 15, 970 (2010) · Zbl 1215.35164
[19] Li, Z. B., Int. J. Nonlinear Sci. Num., 11, 335 (2010)
[20] Li, Z. B.; He, J. H., Nonlinear Sci. Lett. A, 2, 121 (2011)
[21] He, J. H., Thermal Science, 15, S1 (2011)
[22] He, J. H., Thermal Science, 15, S145 (2011)
[23] Jumarie, G., Appl. Math. Lett., 23, 1444 (2010) · Zbl 1202.30068
[24] Jumarie, G., Internat. J. Systems Sci., 6, 1113 (1993)
[25] Jumarie, G., J. Appl. Math. Comput., 24, 31 (2007) · Zbl 1145.26302
[26] Jumarie, G., Appl. Math. Lett., 22, 1659 (2009) · Zbl 1181.44001
[27] Wu, G. C.; He, J. H., Nonlinear Sci. Lett. A, 1, 281 (2010)
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