@article{TMF_2018_197_3_a4,
author = {R. K. Gupta and K. Singla},
title = {Symmetry analysis of variable-coefficient time-fractional nonlinear systems of partial differential equations},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {397--416},
year = {2018},
volume = {197},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a4/}
}
TY - JOUR AU - R. K. Gupta AU - K. Singla TI - Symmetry analysis of variable-coefficient time-fractional nonlinear systems of partial differential equations JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2018 SP - 397 EP - 416 VL - 197 IS - 3 UR - http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a4/ LA - ru ID - TMF_2018_197_3_a4 ER -
%0 Journal Article %A R. K. Gupta %A K. Singla %T Symmetry analysis of variable-coefficient time-fractional nonlinear systems of partial differential equations %J Teoretičeskaâ i matematičeskaâ fizika %D 2018 %P 397-416 %V 197 %N 3 %U http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a4/ %G ru %F TMF_2018_197_3_a4
R. K. Gupta; K. Singla. Symmetry analysis of variable-coefficient time-fractional nonlinear systems of partial differential equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 197 (2018) no. 3, pp. 397-416. http://geodesic.mathdoc.fr/item/TMF_2018_197_3_a4/
[1] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, 204, Elsevier, Amsterdam, 2006 | MR
[2] S. G. Samko, A. A. Kilbas, O. I. Marichev, Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987 | MR
[3] I. Podlubny, An Introduction to Fractional Derivatives, Fractional Differential Equations, to Methods of Their Solution and Some of Their Applications, Fractional Differential Equations, 198, Academic Press, San Diego, CA, 1999 | MR
[4] G. W. Bluman, S. C. Anco, Symmetry and Integration Methods for Differential Equations, Springer, New York, 2002 | MR
[5] P. Olver, Prilozheniya grupp Li k differentsialnym uravneniyam, Mir, M., 1989 | DOI | MR | MR | Zbl | Zbl
[6] L. V. Ovsyannikov, Gruppovoi analiz differentsialnykh uravnenii, M., Nauka, 1978 | MR | MR
[7] E. Buckwar, Y. Luchko, “Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations”, J. Math. Anal. Appl., 227:1 (1998), 81–97 | DOI | MR
[8] R. K. Gazizov, A. A. Kasatkin, S. Yu. Lukaschuk, “Nepreryvnye gruppy preobrazovanii differentsialnykh uravnenii drobnogo poryadka”, Vestn. UGATU, 9:32(21) (2007), 125–135
[9] G. W. Wang, X. Q. Liu, Y. Y. Zhang, “Lie symmetry analysis to the time fractional generalized fifth-order KdV equation”, Commun. Nonlinear Sci. Numer. Simul., 18:9 (2013), 2321–2326 | DOI | MR
[10] Q. Huang, R. Zhdanov, “Symmetries and exact solutions of the time fractional Harry-Dym equation with Riemann–Liouville derivative”, Phys. A, 409 (2014), 110–118 | DOI | MR
[11] K. Singla, R. K. Gupta, “On invariant analysis of some time fractional nonlinear systems of partial differential equations. I”, J. Math. Phys., 57:10 (2016), 101504, 14 pp. | DOI | MR
[12] N. A. Lai, Z. Yi, “Global existence of critical nonlinear wave equation with time dependent variable coefficients”, Commun. Partial Diff. Equations, 37:11 (2012), 1913–1939 | DOI | MR
[13] T. Su, H.-H. Dai, X. Geng, “On the application of a generalized dressing method to the integration of variable-coefficient coupled Hirota equations”, J. Math. Phys., 50:11 (2009), 113507, 12 pp. | DOI | MR
[14] S. Yu. Lukashchuk, A. V. Makunin, “Group classification of nonlinear time-fractional diffusion equation with a source term”, Appl. Math. Comput., 257 (2015), 335–343 | MR
[15] Z. Fu, S. Liu, S. Liu, “New exact solution to the KdV–Burgers–Kuramato equation”, Chaos, Solitons and Fractals, 23:2 (2005), 609–616 | DOI | MR
[16] M. A. Akinlar, A. Secer, M. Bayram, “Numerical solution of fractional Benney equation”, Appl. Math. Inf. Sci., 8:4 (2014), 1633–1637 | DOI | MR
[17] V. S. Kiryakova, Generalized Fractional Calculus and Applications, Pitman Research Notes in Mathematics Series, 301, Longman Scientific Technical, Harlow, 1994 | MR
[18] S. A. El-Wakil, E. M. Abulwafa, E. K. El-Shewy, A. A. Mahmoud, “Time-fractional KdV equation for plasma of two different temperature electrons and stationary ion”, Phys. Plasmas, 18:9 (2011), 092116, 7 pp. | DOI
[19] Y. Pomeau, A. Ramani, B. Grammaticos, “Structural stability of the Korteweg–de Vries solitons under a singular perturbation”, Phys. D, 31:1 (1988), 127–134 | DOI | MR
[20] J. Boussinesq, “Théorie de l'intumescence liquide appelée onde solitaire ou de translation, se propageant dans un canal rectangulaire”, C. R. Acad. Sci. Paris, 72 (1871), 755–778
[21] A. Gill, Dinamika atmosfery i okeana, Mir, M., 1986
[22] A. J. Majda, Introduction to PDEs and Waves for the Atmosphere and Ocean, Courant Lecture Notes in Mathematics, 9, AMS, Providence, RI, 2003 | DOI | MR
[23] K. Singh, R. K. Gupta, “Exact solutions of a variant Boussinesq system”, Internat. J. Eng. Sci., 44:18–19 (2006), 1256–1268 | DOI | MR
[24] M. S. Mohamed, K. A. Gepreel, “Numerical solutions for the time fractional variant Bussinesq equation by homotopy analysis method”, Sci. Res. Essays, 8:44 (2013), 2163–2170 | DOI
[25] H. M. Jaradat, “Dynamic behavior of traveling wave solutions for a class for the time-space coupled fractional KdV system with time-dependent coefficients”, Ital. J. Pure Appl. Math., 36 (2016), 945–958 | MR
[26] K. Singh, R. K. Gupta, “On symmetries and invariant solutions of a coupled KdV system with variable coefficients”, Internat. J. Math. Math. Sci., 2005:23 (2005), 3711–3725 | DOI | MR
[27] H. Zhang, “New exact solutions for two generalized Hirota–Satsuma coupled KdV systems”, Commun. Nonlinear Sci. Numer. Simul., 12:7 (2007), 1120–1127 | DOI | MR
[28] K. Singh, R. K. Gupta, “Lie symmetries and exact solutions of a new generalized Hirota–Satsuma coupled KdV system with variable coefficients”, Internat. J. Eng. Sci., 44:3–4 (2006), 241–255 | DOI | MR