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

Year 2019, Volume: 2 Issue: 2, 139 - 147, 20.12.2019

Gulistan Iskenderoglu Dogan Kaya

https://doi.org/10.33401/fujma.598107

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

Supporting Institution

Istanbul Commerce University

Project Number

22-2018/34

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