Lie symmetry analysis of the time fractional KdV-type equation

Conditional Lie-Bäcklund Symmetry Reductions and Exact Solutions of a Class of Reaction-Diffusion Equations

“…Generally speaking, the obtained solutions cannot be derived within the framework of Lie's classical method and nonclassical method. In addition, it must be pointed out that, for the corresponding equations with certain fractional derivative [25], + + ( ) 2 + ( ) + ( ) = 0, 0 < < 1,…”

Symmetry analysis and conservation laws for the class of time-fractional nonlinear dispersive equation

“…The study of FPDEs through symmetries is quite interesting and significant [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. Therefore, in our present study, we investigate the symmetries of FPDEs and thereby do the analysis.…”

Symmetry solution on fractional equation

“…For construction a symmetry reductions of a fractional equation we investigated the symmetry properties by using the group analysis method and presented the vector fields the equation based on the point symmetry [13,14]. It is shown that our equation could be transformed into a nonlinear fractional ordinary differential equation with the new independent variable.…”

“…As for the methods for solving such equations, there is no effective general method. But there have been formulated and applied methods like Adomian decomposition method [9], differential transform method [10], modified simple equation method [11,12], Lie symmetry analysis [13,14] and so on.…”