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本文利用李群分析方法研究了时间分数阶Boussinesq方程，得到了该方程的李点对称，并把该方程约化为Erdelyi-Kobe分数阶常微分方程. 本文的行文过程也说明了李群分析方法对于约化分数阶非线性发展方程是有效的.We have applied the Lie group analysis method to the time fractional Boussinesq equation. This equation can be reduced to an equation which is related to the Erdelyi-Kober fractional derivative by Lie method as a result. It is shown that the approach introduced here is effective and easy to implement.
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Keywords:
- Lie symmetry analysis method /
- the time fractional Boussinesq equation /
- modied Riemann- Liouville derivative /
- Erdelyi-Kober operator
[1] Ruan H Y, Lou S Y 1992 Acta Phys. Sin. 41 1213 (in Chinese) [阮航宇, 楼森岳 2005 物理学报 41 1213]
[2] Wang L Y 2000 Acta Phys. Sin. 49 181 (in Chinese) [王烈衍 2000 物理学报 49 181]
[3] Clarkson P A, Kruskal M D 1989 Math. Phys. 30 2201
[4] Xin X P, Liu X Q, Zhang L L 2011 Chin. Phys. Lett. 28 1
[5] Li N, Liu X Q 2013 Acta Phys. Sin. 62 0203 (in Chinese) [李宁, 刘希强 2013 物理学报 62 0203]
[6] Yu F J 2011 Chin. Phys. Lett. 28 120201
[7] Ge H X, Liu Y Q, Cheng R J 2012 Chin. Phys. B 21 010206
[8] Khaled A G, Mohamed S M, 2013 Chin. Phys. B 22 010201
[9] Zhang R X, Yang S P 2009 Chin. Phys. B 18 3295
[10] Tao Y J, Huai X L, Li Z G 2006 Chin. Phys. Lett. 23 2487
[11] Wang D F, Zhang J Y, Wang X Y 2013 Chin. Phys. B 22 04507
[12] Chen Y, An H L 2008 Appl. Math. Comput. 200 87
[13] Zhang Q L, Lu L 2011 Chin. Phys. B 20 010510
[14] Lu B 2012 Phys. Lett. A 376 2045
[15] Wang S, Yu Y G 2012 Chin. Phys. Lett. 29 020505
[16] Si G Q, Sun Z Y, Zhang Y B 2011 Chin. Phys. B 20 080505
[17] Buckwar E, Luchko Y 1998 J. Math. Anal. Appl. 227 81
[18] Gazizov R K, Kasatkin A A, Yu S 2007 Vestnik, USATU 9 125 (in Russian)
[19] Djordjevic V D, Atanackovic T M 2008 Comput. Appl. 212 701
[20] Gazizov R K, Kasatkin A A, Lukashchuk S Y 2009 Phys. Scr. T. 136 014
[21] Sahadevan R, Bakkyaraj T 2012 J. Math. Anal. Appl. 393 341
[22] Wang G W, Liu X Q, Zhang Y Y 2013 Commun. Nonl. Sci. Num. Sim 18 2321
[23] Liu Y Q 2012 Journal of Fractional Calculus and Applications 3 1
[24] Momani S, Odibat Z 2007 Phys. Lett. A 365 345
[25] Jumarie G 2006 Comput. Math. Appl. 51 1367
[26] Miller K S, Ross B 1993 Wiley, New York
[27] Podlubny I 1999 Fractional Differential Equations (Academic Press, San Diego CA)
[28] Kiryakova V S 1994 Generalized fractional calculus and applications (Pitman Res. Notesin Math.) 301
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[1] Ruan H Y, Lou S Y 1992 Acta Phys. Sin. 41 1213 (in Chinese) [阮航宇, 楼森岳 2005 物理学报 41 1213]
[2] Wang L Y 2000 Acta Phys. Sin. 49 181 (in Chinese) [王烈衍 2000 物理学报 49 181]
[3] Clarkson P A, Kruskal M D 1989 Math. Phys. 30 2201
[4] Xin X P, Liu X Q, Zhang L L 2011 Chin. Phys. Lett. 28 1
[5] Li N, Liu X Q 2013 Acta Phys. Sin. 62 0203 (in Chinese) [李宁, 刘希强 2013 物理学报 62 0203]
[6] Yu F J 2011 Chin. Phys. Lett. 28 120201
[7] Ge H X, Liu Y Q, Cheng R J 2012 Chin. Phys. B 21 010206
[8] Khaled A G, Mohamed S M, 2013 Chin. Phys. B 22 010201
[9] Zhang R X, Yang S P 2009 Chin. Phys. B 18 3295
[10] Tao Y J, Huai X L, Li Z G 2006 Chin. Phys. Lett. 23 2487
[11] Wang D F, Zhang J Y, Wang X Y 2013 Chin. Phys. B 22 04507
[12] Chen Y, An H L 2008 Appl. Math. Comput. 200 87
[13] Zhang Q L, Lu L 2011 Chin. Phys. B 20 010510
[14] Lu B 2012 Phys. Lett. A 376 2045
[15] Wang S, Yu Y G 2012 Chin. Phys. Lett. 29 020505
[16] Si G Q, Sun Z Y, Zhang Y B 2011 Chin. Phys. B 20 080505
[17] Buckwar E, Luchko Y 1998 J. Math. Anal. Appl. 227 81
[18] Gazizov R K, Kasatkin A A, Yu S 2007 Vestnik, USATU 9 125 (in Russian)
[19] Djordjevic V D, Atanackovic T M 2008 Comput. Appl. 212 701
[20] Gazizov R K, Kasatkin A A, Lukashchuk S Y 2009 Phys. Scr. T. 136 014
[21] Sahadevan R, Bakkyaraj T 2012 J. Math. Anal. Appl. 393 341
[22] Wang G W, Liu X Q, Zhang Y Y 2013 Commun. Nonl. Sci. Num. Sim 18 2321
[23] Liu Y Q 2012 Journal of Fractional Calculus and Applications 3 1
[24] Momani S, Odibat Z 2007 Phys. Lett. A 365 345
[25] Jumarie G 2006 Comput. Math. Appl. 51 1367
[26] Miller K S, Ross B 1993 Wiley, New York
[27] Podlubny I 1999 Fractional Differential Equations (Academic Press, San Diego CA)
[28] Kiryakova V S 1994 Generalized fractional calculus and applications (Pitman Res. Notesin Math.) 301
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