We show how invariant subspace method can be extended to the system time fractional differential equations and construct their exact solutions. Effectiveness of the method has been illustrated by the time fractional Hirota-Satsuma Coupled KdV(HSCKdV) equation.
Topics
Korteweg-de Vries equation
REFERENCES
1.
I.
Podlubny
, Fractional Differential Equations (Academic Press
, New York
, 1999
).2.
D.
Baleanu
, K.
Diethelm
, E.
Scalas
, and J.
Trujillo
, Fractional Calculus Models and Numerical Methods (Series on Complexity
, Nonlinearity and Chaos
) (World Scientific, 2012
).3.
M. S.
Hashemi
and D.
Baleanu
, Communications in Theoretical Physics
65
, p. 11
(2016
).4.
M. S.
Hashemi
, M.
Inc
, B.
Kilic
, and A.
Akgül
, Waves in Random and Complex Media
26
, 259
–271
(2016
).5.
M. S.
Hashemi
and D.
Baleanu
, Journal of Optoelectronics and Advanced Materials
18
(2016
).6.
M. S.
Hashemi
, F.
Bahrami
, and R.
Najafi
, Optik-International Journal for Light and Electron Optics
138
, 240
–249
(2017
).7.
G.
Wang
and M. S.
Hashemi
, Pramana
88
, p. 7
(2017
).8.
W.-X.
Ma
, Sci. China Math.
55
, 1769
–1778
(2012
).9.
W.-X.
Ma
and Y.
Liu
, Commun. Nonlinear Sci. Numer. Simul.
17
, 3795
–3801
(2012
).10.
Y.
Yildirim
, E.
Yasar
, and A. R.
Adem
, Nonlinear Dynam.
89
, 2291
–2297
(2017
).11.
E.
Yasar
, Y.
Yildirim
, and M. K.
Chaudry
, Results in Physics
6
, 322
–328
(2016
).12.
13.
Y.
Yildirim
and E.
Yasar
, Chinese Physics B
26
(7
) (2017
).14.
I. B.
Giresunlu
, Y. Saglam
Ozkan
, and E.
Yasar
, Mathematical Methods in the Applied Sciences
(2017
).15.
Z.
Ganji
, D.
Ganji
, and Y.
Rostamiyan
, Applied Mathematical Modelling
33
, 3107
–3113
(2009
).16.
V. A.
Galaktionov
and S. R.
Svirshchevskii
, Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics, Chapman & Hall/CRC Applied Mathematics and Nonlinear Science
(Chapman Hall/CRC
, 2007
).17.
A.
Ouhadan
and E.
El Kinani
, British Journal of Mathematics & Computer Science
15
(2016
).18.
R.
Gazizov
and A.
Kasatkin
, Computers & Mathematics with Applications
66
, 576
–584
(2013
).19.
20.
R.
Sahadevan
and P.
Prakash
, Communications in Nonlinear Science and Numerical Simulation
42
, 158
–177
(2017
).21.
R.
Sahadevan
and T.
Bakkyaraj
, Fractional Calculus and Applied Analysis
18
, 146
–162
(2015
).
This content is only available via PDF.
© 2018 Author(s).
2018
Author(s)
You do not currently have access to this content.