On Fractional Backward Differential Formulas Methods for Fractional Differential Equations with Delay

In this paper, fractional backward differential formulas are presented for the numerical solution of fractional delay differential equations in Caputo sense. We focus on linear equations. Our investigation is focused on stability properties of the numerical methods and we determine stability regions for the fractional delay differential equations. Also we proposed the dependence of the solution on the parameters of the equation and conclude with a numerical treatment and examples based on the adaptation of a fractional backward differential formulas methods to the delay case. Numerical experiments are provided to illustrate potential and limitations of the different methods under investigation.