Numerical analysis of the initial conditions in fractional systems

•Analysis of initial conditions from the viewpoint of numerical approximations.•Statistical study of the impact of initial conditions in fractional systems.•Numerical benchmark of initialization in fractional dynamics.

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.