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Analysis and numerical methods for fractional differential equations with delay. (English) Zbl 1291.65214
Summary: 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.

##### MSC:
 65L05 Numerical methods for initial value problems 34A08 Fractional ordinary differential equations and fractional differential inclusions 34K28 Numerical approximation of solutions of functional-differential equations (MSC2010) 34K06 Linear functional-differential equations
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