TY  - JOUR
T1  - Symmetry Analysis and Conservation Laws of the Boundary Value Problems for Time-Fractional Generalized Burgers' Differential Equation
AU  - Iskenderoglu, Gulistan
AU  - Kaya, Dogan
PY  - 2019
DA  - December
Y2  - 2019
DO  - 10.33401/fujma.598107
JF  - Fundamental Journal of Mathematics and Applications
JO  - Fundam. J. Math. Appl.
PB  - Fuat USTA
WT  - DergiPark
SN  - 2645-8845
SP  - 139
EP  - 147
VL  - 2
IS  - 2
LA  - en
AB  - 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.
KW  - Boundary value problem
KW  - Conservation laws
KW  - Generalized Burgers' equation
KW  - Lie groups method
KW  - Riemann--Liouville derivative
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UR  - https://doi.org/10.33401/fujma.598107
L1  - https://dergipark.org.tr/en/download/article-file/889137
ER  -