A Lie Symmetry Study Of A Class Of Time Fractional Equations

In recent decades,the fractional differential equation ave used to describe the problem in thermodynamic system,rheology,mechanical system,signal processing and system identification and the other field of applications.It is very important to study group-invariant solutions,and symmetry re-duction for fractional differential equation.Lie symmetry method can reduce the amount of the calculations,and it can help us solve the equations which were too difficult to solve.In this dissertation,we study three fractional differential equations by using the classical Lie symmetry method,with the definition of the revised Riemann-Liouville fractional integration.The main contents are given as follows:For the 1+1 time fractional gas dynamics equation,me find the equivalent equations of the original equation by using Lie single-parameter transformation.The exact solutions of the original equation can be derived by solving the equivalent equations.The symmetries of the 2+1 fractional heat-like equation are obtained by Lie symmetry method.Then we choose some simple symmetries to simplify the equation,and obtain some group invariant solutions of the heat-like equation.We studythe Boussinesq-Burgers fractional system by Lie symmetry method.With the symmetries the one-parameter group of transformations and some group-invariant solutions of the system are obtained.