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**A survey on semilinear differential equations and inclusions involving Riemann-Liouville fractional derivative.**
*(English)*
Zbl 1182.34103

This review paper focuses on semilinear functional differential equations containing Riemann-Liouville fractional derivatives. The paper’s main contribution is that it brings together and establishes a range of results on basic theory for different classes of problem. For semilinear functional differential equations of both classical and neutral type, consideration is given first to equations with finite delay and then to equations with infinite delay. There is a review of existence results and an example in each case. Finally the authors consider perturbed differential equations and inclusions, and provide some existence results on ordered Banach spaces.

Reviewer: Neville Ford (Chester)

### MSC:

34K37 | Functional-differential equations with fractional derivatives |

34K40 | Neutral functional-differential equations |

34K30 | Functional-differential equations in abstract spaces |

34K09 | Functional-differential inclusions |

### Keywords:

semilinear functional differential equations; fractional derivatives; neutral equations; inclusions
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\textit{R. P. Agarwal} et al., Adv. Difference Equ. 2009, Article ID 981728, 47 p. (2009; Zbl 1182.34103)

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