Study On Solutions Of Three Kinds Of Time Fractional Partial Differential Equations

Equations containing fractional derivatives or fractional integrals are called fractional differential equations.Compared with integer differential equations,it can describe some dynamic processes of diffusion and conduction more accurately.Fractional differential equations are of increasing importance in many fields of applied science such as mechanics,materials science,signal image processing and so on.As an important branch of fractional differential equations,fractional partial differential equations are increasingly used in practical engineering fields such as physics finance and so on.Solving fractional partial differential equations has become an urgent and important topic.This paper first introduces the research background and research status of three kinds of time-fractional partial differential equations,which are time-fractional two-component evolutionary system of order 2,time-fractional Drinfeld-Sokolov-Wilson system,and time-fractional Boussinesq-Burger equations.Besides,the definition of fractional differential operator and some important properties are given.Secondly,for time-fractional two-component evolutionary system of order 2,sub-equation method,tanh method,improved Kudryashov method,(G'/G)-expansion method,and the Exp-function method are used to obtain the exact solutions.In addition,the relationship between these solutions is also analyzed.Finally,coupled fractional reduced differential transform method is introduced.Using this method,the approximate solution of time-fractional Drinfeld-Sokolov-Wilson system is obtained,and the obtained results are compared with the approximate solutions obtained by residual power series method.It shows that coupled fractional reduced differential transform method is also an effective method to solve such time-fractional partial differential equations.The approximate solution of the time-fractional Boussinesq-Burger equations is obtained by this method.The obtained results are compared with the approximate solutions obtained by the homotopy perturbation method.These results show that coupled fractional reduced differential transform method is also an efficient method to solve this equation.