Invariant analysis of time fractional generalized Burgers and Korteweg-de Vries equations

Journal of Mathematical Analysis and Applications

Volumn 393, Issue 2, 2012, Pages 341-347

  Sahadevan, R ^a   Bakkyaraj, T ^a  

^a UNIVERSITY OF MADRAS   (India)

Author keywords

Erd lyi Kober operators; Fractional differential equations; Lie symmetry analysis; Riemann Liouville fractional derivative

Indexed keywords

EID: 84860915405     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2012.04.006     Document Type: Article

References (30)

1. Bluman G.W., Anco S. Symmetry and Integration Methods for Differential Equations 2002, Springer-Verlag, Heidelburg.
2. Ibragimov N.H. CRC Handbook of Lie Group Analysis of Differential Equations-Symmetries, Exact Solutions and Conservation Laws 1994, vol. 1. CRC Press, New York.
3. Lakshmanan M., Kaliappan P. Lie transformations, nonlinear evolution equations and Painlevé forms. J. Math. Phys. 1983, 24:795.
4. Olver P.J. Applications of Lie Groups to Differential Equations 1986, Springer-Verlag, Heidelberg.
5. Ovsiannikov L.V. Group Analysis of Differential Equations 1982, Academic Press, New York.
6. P. Winternitz, Lie groups and solutions of nonlinear partial differential equations, in: Lecture Notes in Physics, CRM-1841, Canada, 1993.
7. Fokas A.S. Symmetries and integrability. Stud. Appl. Math. 1987, 77:253.
8. A.B. Mikhailov, A.B. Shabat, V.V. Sokolov, The symmetry approach to classification of integrable equation, in: What is Integrability?, Springer Series on Nonlinear Dynamics, Berlin, 1991, pp. 115-184.
9. Levi D., Winternitz P. Continuous symmetries of discrete equations. Phys. Lett. A 1991, A152:335-340.
10. Maeda S. Canonical structure and symmetries for discrete systems. Math. Japon. 1980, 25:405-420.
11. Sahadevan R., Rajakumar S. Bilinear, trilinear forms and exact solution of certain fourth order integrable difference equations. J. Math. Phys. 2008, 49:033517.
12. Hilfer R. Applications of Fractional Calculus in Physics 2000, World Scientific, Singapore.
13. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Amsterdam, The Netherlands, 2006.
14. Miller K.S., Ross B. An Introduction to the Fractional Calculus and Fractional Differential equations 1993, Wiley, New York.
15. Samko S., Kilbas A.A., Marichev O. Fractional Integrals and Derivatives: Theory and Applications 1993, Gordon and Breach science, Yverdon, Switzerland.
16. Meerschaert M.M., Scheffler H.P., Tadjeran C. Finite difference methods for two-dimensional fractional dispersion equation. J. Comput. Phys. 2006, 211:249-261.
17. Momani S., Odibat Z. Analytical solution of a time fractional Navier-Stokes equation by Adomian decomposition method. Appl. Math. Comput. 2006, 177:488-494.
18. He J.H. Approximate analytical solution for seepage flow with fractional derivatives in porous media. Comput. Methods Appl. Mech. Eng. 1998, 167:57-68.
19. Momani S., Odibat Z. Homotopy perturbation method for nonlinear partial differential equations of fractional order. Phys. Lett. A 2007, 365:345-350.
20. Bagley R., Torvik P. A theoretical basis for the application of fractional calculus to visco-elasticity. J. Rheol. 1983, 27(3):201-210.
21. Momani S., Odibat Z. Generalised differential transform method for linear partial differential equations of fractional order. Appl. Math. Lett. 2008, 21(2):194-199.
22. Diethelm K. An algorithm for the numerical solution for differential equation of fractional order. Electron. Trans. Numer. Anal. 1997, 5:1-6.
23. Yuan L., Agrawal O.P. A numerical scheme for dynamic systems containing fractional derivatives. J. Vib. Acoust. 2002, 124:321-324.
24. Gazizov R.K., Kasatkin A.A., Lukashchuk S.Yu. Continuous transformation groups of fractional differential equations. Vestnik, USATU 2007, 9:125-135. (in Russian).
25. Gazizov R.K., Kasatkin A.A., Lukashchuk S.Yu. Symmetry properties of fractional diffusion equations. Phys. Scr. 2009, T136:014016.
26. Buckwar E., Luchko Y. Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations. J. Math. Anal. Appl. 1998, 227:81-97.
27. Djordjevic V.D., Atanackovic T.M. Similarity solutions to nonlinear heat conduction and Burgers/Korteweg-deVries fractional equations. J. Comput. Appl. Math. 2008, 212:701-714.
28. Podlubny I. Fractional Differential Equations 1999, Academic Press, San Diego, CA.
29. Oldham K.B., Spanier J. The Fractional Calculus 1974, Academic Press.
30. Kiryakova V. Generalised Fractional Calculus and Applications. Pitman Res. Notes in Math. 1994, vol. 301.