episciences.org_9283_1669865981
1669865981
episciences.org
raphael.tournoy+crossrefapi@ccsd.cnrs.fr
episciences.org
Communications in Mathematics
23361298
05
12
2022
Volume 30 (2022), Issue 1
Invariance analysis and some new exact analytic solutions of the timefractional coupled DrinfeldSokolovWilson equations
Chauhan Astha
Arora Rajan
In this work, the fractional Lie symmetry method is used to find the exact solutions of the timefractional coupled DrinfeldSokolovWilson equations with the RiemannLiouville fractional derivative. Timefractional coupled DrinfeldSokolovWilson equations are obtained by replacing the firstorder time derivative to the fractional derivatives (FD) of order $\alpha$ in the classical DrinfeldSokolovWilson (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$\acute{e}$lyiKober fractional differential operator. Also, we have obtained the exact solution of FCDSW equations and shown the effects of noninteger 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.
05
12
2022
9283
https://creativecommons.org/licenses/by/4.0
10.5281/zenodo.6424753
10.46298/cm.9283
https://cm.episciences.org/9283

https://cm.episciences.org/9283/pdf