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

Agarwal, Ravi P.; Belmekki, Mohammed; Benchohra, Mouffak

Adv. Difference Equ. 2009, Article ID 981728, 47 p. (2009).

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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