A Legendre wavelet collocation method for 1D and 2D coupled time-fractional nonlinear diffusion system

A Legendre wavelet collocation method is proposed for solving a nonlinear coupled time fractional diffusion system. We have formulated a Riemann-Liouville fractional integral operator for Legendre wavelet (RLFIO-L) adopting the definition of Riemann-Liouville fractional integral operator combined with the Laplace transformation. Both the time and space variables are discretized in terms of the Legendre wavelet and RLFIO-L. The nonlinear coupled diffusion system is quasi-linearized by making use of the Newton's method. For theoretical concerns, the upper bound of error norm of the proposed method is estimated. Some numerical experiments are presented to authenticate the computational efficacy of the method