INVARIANT ANALYSIS AND CONSERVATION LAWS FOR THE SPACE-TIME FRACTIONAL KDV-LIKE EQUATION
Jian‐Gen Liu, Xiao‐Jun Yang, Yi‐Ying Feng, Lu‐Lu Geng
Abstract
Fractional calculus plays an essential role in describing nonlinear phenomena appears in applied sciences. In this article, we handle mainly the Korteweg-de Vries (KdV)-like equation which can be used to depicted the shallow water waves evolution mechanism in the sense of the space-time fractional derivative of the Riemann-Liouville. Firstly, on the basis of the Lie symmetry analysis technology, the symmetry of this considered model was constructed. Then, this equation can be changed into a fractional ordinary differential equation with the help of the Erdélyi-Kober fractional operators. Subsequently, the one-parameter group of Lie point transformation and a special type exact solution of this researched model were also obtained. Lastly, based on the nonlinear self-adjointness, conservation laws of the space-time fractional KdV-like equation can be found. These results can provide us with a new scheme for studying space-time fractional differential equations.