A new meshless method of solving the distributed-order time-fractional mobile-immobile equations

A new method is introduced by combining neural network’s huge expressive power with technologies of the minimum residual approximate solutions (MRASs). In spatial direction, a single hidden layer neural network makes the construction of bases functions easier. The cost of calculations becomes acceptable in high dimensions space using the technologies of the MRASs. And this paper establish approximation and convergence order theories based on neural network.