Application Of Extended Trial Equation Method And Modified Auxiliary Equation Method In Solving Nonlinear Fractional Evolution Equations

In this topic,we mainly use related knowledge of differential equations,traveling wave transformation,homogeneous balance principle,modified auxiliary equation method,extended trial equation method and Matlab calculation software to solve the space-time(2+1)-dimensional Maccari equations and space-time(3+1)-dimensional Burger equation with the conformable fractional derivative.Based on the research background,research trends,the purpose,meaning and main work,the first chapter focuses on the conformable fractional derivative,nonlinear fractional evolution equations,extended trial equation method and modified auxiliary equation method.Aiming at the topic of solving the space-time(2+1)-dimensional Maccari equations with the conformable fractional derivative in chapter 2.We use traveling wave transformation and the principle of homogeneous balance to judge the solution to have the following two forms:(?)and(?).And then use the trial equation Y’(φ)=h0+h1Y(φ)+h2Y2(φ)+h3Y3(φ)and the extended trial equation method to solve the equations.Aiming at the topic of solving the space-time(3+1)-dimensional Burger equation with the conformable fractional derivative in chapter 3.we use traveling wave transformation and the principle of homogeneous balance to judge the solution to have the following form:(?).Then the equation is solved with the help of auxiliary equation(?)and the modified auxiliary equation method.In chapter 4,this article mainly summarizes the main research content and conclusions.