A numerical solution of fractional reaction–convection–diffusion for modeling PEM fuel cells based on a meshless approach

The purpose of this contribution is to present or implement generalized finite difference method (GFDM) for the first time in order to solve the reaction convection Diffusion equation (FRCDE) model. The FRCDE equations are nonlinear time fractional differential equations that can be used to describe mathematical models in physics and engineering, such as fuel cells and transport in inhomogeneous media. This model is a generalization of the classical RCDE, with time terms considered by Caputo derivative sense for 0<α(x,t)<1. The meshless GFDM, in conjunction with the ϑ-weighted finite difference method, is developed to approximate processes in the spatial direction. GFDM is based on the Taylor series expansion and the moving least squares (MLS) method to evaluate the derivatives of unknown variables. The proposed method, as a truly meshless approach, is very promising in the numerical approximation of engineering problems within convex, non-convex, irregular, and regular domains (complex domains). The reliability and accuracy of the proposed method are shown by considering a variety of computational domains. The sensitivity of the selection of local collocation points and ϑ is also reported.