Study On The Solutions Of Several Classes Of Fractional Order Nonlinear Partial Differential Equations

Fractional order nonlinear partial differential equations have been widely used in physics,chemistry,engineering and other fields.Finding the analytic solution or the exact solution of the nonlinear development equation of fractional order has always been an important topic for mathematical researchers.In this paper,the exact solutions of some kinds of fractional order nonlinear partial differential equations(groups)are studied by Kudryashov method and its derivation methods.With the help of fractional order complex transformation method,their exact solutions are successfully obtained,thus the solution system of the relevant equations is expanded,which provides a new possibility for the study of the equations.This paper mainly introduces the Kudryashov method and its derivation methods in detail.Which include the kudryashov method,the modified Kudryashov method,the generalized Kudryashov method,and the generalized tanh-coth method.Secondly,on the basis of the method of fractional complex transformation,these methods are used to solve the exact solutions of the time-space fractional Whitham-Broer-Kuap equations,the time-space fractional Caudrcy-Dold-Gibbon-Sawada-Kotcra equation,the space-time fractional Equal-Width equation,the space-time fractional BenjaminBona-Mahony equation,(3+1)the spatial-time fractional modified Zakharov-Kuznestov equation,the fractional coupled Drinfel'd-Sokolov-Wilson equations,etc.This is of great practical significance and strong research value for methods such as Kudryashov method and its derivative methods to solve the exact solution of fractional-order nonlinear partial differential equations(groups).The last part is mainly about summary and prospect.The last part is mainly about the research results and the innovations.It first summarizes the current research results,then summarizes the main innovations.Finally,in the prospect section,some suggestions for solving the exact solution of fractional order nonlinear partial differential equations(groups)are given.