Symmetry Analysis and Conservation Laws of the Boundary Value Problems for Time-Fractional Generalized Burgers` Differential Equation

Authors : Gulistan ISKENDEROGLU, Dogan KAYA

Pages : 139-147

Doi:10.33401/fujma.598107

View : 22 | Download : 12

Publication Date : 2019-12-20

Article Type : Research Paper

Abstract :Many physical phenomena in nature can be described or modeled via a differential equation or a system of differential equations. In this work, we restrict our attention to research a solution of fractional nonlinear generalized Burgers` differential equations.  Thereby we find some exact solutions for the nonlinear generalized Burgers` differential equation with a fractional derivative, which has domain as $\mathbb{R}^2\times\mathbb{R}^+$. Here we use the Lie groups method. After applying the Lie groups to the boundary value problem we get the partial differential equations on the domain $\mathbb{R}^2$ with reduced boundary and initial conditions. Also, we find conservation laws for the nonlinear generalized Burgers` differential equation.
Keywords : Boundary value problem, Conservation laws, Generalized Burgers` equation, Lie groups method, Riemann Liouville derivative