10.46298/cm.9283
https://cm.episciences.org/9283
Chauhan Astha
Chauhan Astha
Arora Rajan
Arora Rajan
Invariance analysis and some new exact analytic solutions of the time-fractional coupled Drinfeld-Sokolov-Wilson equations
In this work, the fractional Lie symmetry method is used to find the exact solutions of the time-fractional coupled Drinfeld-Sokolov-Wilson equations with the Riemann-Liouville fractional derivative. Time-fractional coupled Drinfeld-Sokolov-Wilson equations are obtained by replacing the first-order time derivative to the fractional derivatives (FD) of order $\alpha$ in the classical Drinfeld-Sokolov-Wilson (DSW) model. Using the fractional Lie symmetry method, the Lie symmetry generators are obtained. With the help of symmetry generators, FCDSW equations are reduced into fractional ordinary differential equations (FODEs) with Erd$\acute{e}$lyi-Kober fractional differential operator. Also, we have obtained the exact solution of FCDSW equations and shown the effects of non-integer order derivative value on the solutions graphically. The effect of fractional order $\alpha$ on the behavior of solutions is studied graphically. Finally, new conservation laws are constructed along with the formal Lagrangian and fractional generalization of Noether operators. It is quite interesting the exact analytic solutions are obtained in explicit form.
episciences.org
Attribution 4.0 International (CC BY 4.0)
2022-04-05
2022-05-12
2022-05-12
eng
journal article
10.5281/zenodo.6424753
2336-1298
https://cm.episciences.org/9283/pdf
VoR
application/pdf
Communications in Mathematics
Volume 30 (2022), Issue 1
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