Analysis and Numerical Methods for Fractional Differential Equations with Delay

Journal of Computational and Applied Mathematics, 252 (2013), 159-168
http://dx.doi.org/10.1016/j.cam.2012.06.034

In this paper, we consider fractional differential equations with delay. We focus on linear equations. We summarise existence and uniqueness theory based on the method of steps and we give a theorem on the propagation of derivative discontinuities. We discuss 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 difference method to the delay case.