Singular and non-topological soliton solutions for nonlinear fractional differential equations

doi:10.1088/1674-1056/24/10/100201

摘要/Abstract

摘要：

In this article, the fractional derivatives are described in the modified Riemann-Liouville sense. We propose a new approach, namely an ansatz method, for solving fractional differential equations (FDEs) based on a fractional complex transform and apply it to solve nonlinear space-time fractional equations. As a result, the non-topological as well as the singular soliton solutions are obtained. This method can be suitable and more powerful for solving other kinds of nonlinear fractional FDEs arising in mathematical physics.

关键词: solitons, ansatz method, the space-time fractional Boussinesq equation, the space-time fractional (2+1)-dimensional breaking soliton equations

Abstract:

Key words: solitons, ansatz method, the space-time fractional Boussinesq equation, the space-time fractional (2+1)-dimensional breaking soliton equations

中图分类号: (Partial differential equations)

02.30.Jr

05.45.Yv (Solitons)

Ozkan Guner. Singular and non-topological soliton solutions for nonlinear fractional differential equations[J]. 中国物理B, 2015, 24(10): 100201-100201.

Ozkan Guner. Singular and non-topological soliton solutions for nonlinear fractional differential equations[J]. Chin. Phys. B, 2015, 24(10): 100201-100201.

参考文献 55

[1]	Podlubny I 1999 Fractional Differential Equations (California: Academic Press)
[2]	Klafter J, Lim S C and Metzler R 2011 Fractional Dynamics in Physics: Recent Advances (Singapore: World Scientific)
[3]	Tarasov V E 2011 Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media (Berlin: Springer)
[4]	Mainardi F 2010 Fractional Calculus and Waves in Linear Viscoelasticity (London: Imperial College Press)
[5]	Zheng B 2012 Commun. Theor. Phys. 58 623
[6]	Bekir A and Guner O 2013 Chin. Phys. B 22 110202
[7]	Zayed E M E and Arnous A H 2014 European Journal of Academic Essays 1 6
[8]	Taghizadeh N, Mirzazadeh, M and Farahrooz F 2013 J. Math. Anal. Appl. 374 549
[9]	Bekir A, Guner O and Unsal O 2015 J. Comp. Nonlinear Dyn. 10 463
[10]	Zayed E M E and Amer Y A 2014 Int. J. Phys. Sci. 9 174
[11]	Zhang S and Zhang H Q 2011 Phys. Lett. A 375 1069
[12]	Alzaidy J F 2013 British J. Math. & Comput. Sci. 3 153
[13]	Tong B, He Y, Wei L and Zhang X 2012 Phys. Lett. A 376 2588
[14]	Bekir A, Guner O and Cevikel A C 2013 Abstract and Applied Analysis 2013 426462
[15]	Guner O and Cevikel A C 2014 The Scientific World Journal 2014 489495
[16]	Guner O and Bekir A 2015 Int. J. Biomath. 8 1550003
[17]	Liu W and Chen K 2013 Pramana J. Phys. 81 3
[18]	Guner O and Eser D 2014 Adv. Math. Phys. 2014 456804
[19]	Bulut H, Baskonus, H M, Pandir Y 2013 Abstract and Applied Analysis 2013 636802
[20]	Ege S M and Misirli E 2014 Advances in Difference Equations 2014 135
[21]	Inc M and Kilici B 2014 Waves in Random and Complex Media 24 393
[22]	Mirzazadeh M 2015 Pramana J. Phys. 85 17
[23]	Savescu M, Khan K R, Kohl R, Moraru L, Yildirim A and Biswas A 2013 J. Nanoelectron. Optoelectron. 8 208
[24]	Kohl R, Biswas A, Milovic D and Zerrad E 2008 Opt. Laser Technol. 40 647
[25]	Triki H and Biswas A 2011 Math. Methods Appl. Sci. 3 958
[26]	Bekir A, Aksoy E and Guner O 2013 J. Nonlinear Opt. Phys. & Mater. 22 1350015
[27]	M. Eslami and M. Mirzazadeh 2013 Eur. Phys. J. Plus 128 1
[28]	Bekir A and Guner O 2013 Ocean Engineering 74 276
[29]	Boubir B, Triki H and Wazwaz A M 2013 Appl. Math. Model. 37 420
[30]	Bekir A, Aksoy E and Guner O 2012 Phys. Scr. 85 035009
[31]	Triki H and Wazwaz A M 2011 Appl. Math. Comput. 217 8846
[32]	Samko S G, Kilbas A A and Marichev O I 1993 Fractional Integrals and Derivatives: Theory and Applications (Switzerland: Gordon and Breach Science Publishers)
[33]	Caputo M 1967 Geophys. J. Royal Astronom. Soc. 13 529
[34]	Jumarie G 2006 Comput. Math. Appl. 51 1367
[35]	Tarasov V E 2013 Commun. Nonlinear Sci. Numer. Simul. 18 2945
[36]	Jumarie G 2009 Appl. Math. Lett. 22 378
[37]	Hartley T and Lorenzo C F 2002 Nonlinear Dyn. 29 201
[38]	Kilbas A A, Srivastava H M and Trujillo. J J 2006 Theory and Applications of Fractional Differential Equations (Amsterdam: Elsevier)
[39]	He J H, Elegan S K and Li Z B 2012 Phys. Lett. A 376 257
[40]	Saad M, Elagan S K, Hamed Y S and Sayed M 2013 Int. J. Basic & Appl. Sci. 13 23
[41]	Elghareb T, Elagan S K, Hamed Y S and Sayed M 2013 Int. J. Basic & Appl. Sci. 13 19
[42]	Jafari H, Tajadodi H, Baleanu D, Al-Zahrani A A, Alhamed Y A and Zahid A H 2013 Romanian Rep. Phys. 65 1119
[43]	Triki H and Wazwaz A M 2009 Phys. Lett. A 373 2162
[44]	Ebadi G and Biswas A 2011 Math. Comput. Model. 53 694
[45]	Biswas A, Triki H and Labidi M 2011 Physics of Wave Phenomena 19 24
[46]	Bekir A and Guner O 2013 Pramana J. Phys. 81 203
[47]	Chowdhury A and Biswas A 2012 Math. Sci. 6 42
[48]	Inc M, Ulutas E and Biswas A 2013 Chin. Phys. B 22 060204
[49]	Song M, Liu Z, Zerrad Z and Biswas A 2013 Appl. Math. Inf. Sci. 7 1333
[50]	Wen C and Zheng B 2013 Wseas Transactions on Mathematics 5 12
[51]	Bekir A and Guner O 2014 Int. J. Nonlinear Sci. Numer. Simul. 15 463
[52]	Zhang S 2007 Phys. Lett. A 368 470
[53]	Peng Y Z and Krishnan E V 2005 Commun. Theor. Phys. 44 807
[54]	Ren Y J, Liu S T and Zhang H Q 2006 Commun. Theor. Phys. 45 15
[55]	Chen Y, Li B and Zhang H Q 2003 Commun. Theor. Phys. 40 137