In this paper, the time fractional Fordy–Gibbons equation is investigated with Riemann–Liouville derivative. The equation can be reduced to the Caudrey–Dodd–Gibbon equation, Savada–Kotera equation and the Kaup–K...In this paper, the time fractional Fordy–Gibbons equation is investigated with Riemann–Liouville derivative. The equation can be reduced to the Caudrey–Dodd–Gibbon equation, Savada–Kotera equation and the Kaup–Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method.展开更多
基金Supported by the Fundamental Research Funds for Key Discipline Construction under Grant No.XZD201602the Fundamental Research Funds for the Central Universities under Grant Nos.2015QNA53 and 2015XKQY14+2 种基金the Fundamental Research Funds for Postdoctoral at the Key Laboratory of Gas and Fire Control for Coal Minesthe General Financial Grant from the China Postdoctoral Science Foundation under Grant No.2015M570498Natural Sciences Foundation of China under Grant No.11301527
文摘In this paper, the time fractional Fordy–Gibbons equation is investigated with Riemann–Liouville derivative. The equation can be reduced to the Caudrey–Dodd–Gibbon equation, Savada–Kotera equation and the Kaup–Kupershmidt equation, etc. By means of the Lie group analysis method, the invariance properties and symmetry reductions of the equation are derived. Furthermore, by means of the power series theory, its exact power series solutions of the equation are also constructed. Finally, two kinds of conservation laws of the equation are well obtained with aid of the self-adjoint method.
