Monotone iterative solutions for nonlinear fractional differential systems with deviating arguments

•Consider the nonlinear fractional differential systems with deviating arguments.•Establish the existence result of solution.•Introduce a numerical iterative scheme.

By means of the monotone iterative technique, we consider the nonlinear fractional differential systems with deviating arguments, introduce two well-defined monotone sequences of solutions which converge uniformly to the solutions of the systems, and then the existence result of solution for the systems is established. A numerical iterative scheme is introduced to obtain an accurate approximate solution for the systems. As an application, an example is presented to demonstrate the accuracy and efficiency of the new approach.