EXTENDING OPERATOR METHOD TO LOCAL FRACTIONAL EVOLUTION EQUATIONS IN FLUIDS

Ibis paper is aimed to solve non-linear local fractional evolution equations in fluids by extending the operator method proposed by Zenonas Navickas [15]. 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 ODE is obtained by the extended operator method. Finally, with the help of the obtained solution in the form of operator representation and the travelling-wave transformations, the local fractional Kadomtsev-Petviashvili (KP) equation and the fractional Benjamin-Bona-Alahoney (BBM) equation are solved. It is shown that the extended operator method can he used for solving some other non-linear local fractional evolution equations in fluids.