摘要
In this work, we study a system of autonomous fractional differential equations. The differential operator is taken in the Caputo sense. Using the monotone iterative technique combined with the method of upper and lower solutions, we investigate the existence and uniqueness of solutions for coupled system which are nonlinear fractional differential equations, moreover, we obtain the dependence of the solution on the initial values. In addition, we give an important example that is a two-patch subdiffusive predator-prey metapopulation model, investigate the solvability and give the numerical results with this model. The numerical simulation indicates that the results of the suhdiffusive model approximate to the two-patch predator-prey metapopulation model with the order a approach to 1.
