Lie Symmetry Of A Class Of Time Fractional Equations

Applying Lie symmetry method to the fractional order partial differential e-quation is studied in this article.Fractional order differential equation is widely used to describe the thermodynamic system,mechanical system,signal processing and system identification problem in the field of application,and can describe the memory and genetic characteristics of materials and processes.For time fraction-al partial difference equation,the research group invariant solution and symmetry reduction,can reduce the computation of solving equations.This paper consists of three chapters:The first chapter is introduction,which mainly introduces the research back-ground and development of fractional order calculus present situation,the research background and current situation of the development of Lie group,and the theo-ry of Lie group of symmetry in partial differential equation and the application of fractional order partial differential equation.The second chapter is preliminary knowledge,which mainly introduces the definition of fractional calculus,and the basic concepts and properties of Lie group,such as single parameter transformation group,prolongation and vector field.In the third chapter,the research is focus on Lie symmetry for time fractional Cahn-Allen equation and fractional Sharma-Tasso-Olver equation.According to the calculation of the prolongation and the matching vector field,finally,the invariant solution is obtained by using the result of the vector field.