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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 41 1213]
[2] Wang L Y 2000 Acta Phys. Sin. 49 181 (in Chinese) [王烈衍 2000 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 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 41 1213]
[2] Wang L Y 2000 Acta Phys. Sin. 49 181 (in Chinese) [王烈衍 2000 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 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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