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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.

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
Full Text: DOI
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