Conformable bilinear neural network method: a novel method for time-fractional nonlinear partial differential equations in the sense of conformable derivative

This paper introduces a novel method called conformable bilinear neural network method to search for exact analytical solutions of time-fractional nonlinear partial differential equations under the conformable sense. This is the first time to give bilinear forms of the time-fractional nonlinear partial differential equations in the conformable sense and to combine them with the neural network model to obtain exact analytical solutions. To demonstrate the superiority, generality and flexibility of the proposed method, we investigate three types of conformable time-fractional nonlinear partial differential equations, including fifth-order Sawada-Kotera equation and (3+1)-dimensional Jimbo-Miwa equation. Numerous solutions of arbitrary function of these equations can be obtained by the proposed method. In addition, we draw 3D plots, curve plots, contour plots and density plots to observe the self-similar characteristics and abundant dynamical behavior of these solutions.