The numerical solution of time fractional generalized Benjamin-Bona-Mahony equation via the Sinc functions

The aim of this paper is to analyze a numerical method for solving the time fractional Benjamin-Bona-Mahony (BBM) equation. The time variable has been discretized by using the finite forward difference procedure. The unconditionally stable semi-discrete formula has been proven. Then we apply the Sinc collocation method to approximate the solution of the semi-discrete scheme. The exponential convergence rate of the Sinc method has also been proven. To show the efficiency of the proposed method, two examples were given. Numerical results verified the theoretical results and illustrate the efficiency and accuracy of the method compared with other methods.