TY - JOUR
TI - Extending operator method to local fractional evolution equations in fluids
AU - Zhang Sheng
AU - Zhao Sen
AU - Zhang Yue
JN - Thermal Science
PY - 2019
VL - 23
IS - 6
SP - 3759
EP - 3766
PT - Article
AB - This paper is aimed to solve non-linear local fractional evolution equations  in fluids by extending the operator method proposed by Zenonas Navickas.  Firstly, we give the definitions of the generalized operator of local  fractional differentiation and the multiplicative local fractional operator.  Secondly, some properties of the defined operators are proved. Thirdly, a  solution in the form of operator representation of a local fractional  ordinary differential equation is obtained by the extended operator method.  Finally, with the help of the obtained solution in the form of operator  representation and the fractional complex transform, the local fractional  Kadomtsev-Petviashvili (KP) equation and the fractional  Benjamin-Bona-Mahoney (BBM) equation are solved. It is shown that the  extended operator method can be used for solving some other non-linear local  fractional evolution equations in fluids.