Semilinear fractional order integro-differential equations with infinite delay in Banach spaces. (English) Zbl 1299.26008

Aissani, Khalida; Benchohra, Mouffak

Arch. Math., Brno 49, No. 2, 105-117 (2013).

The authors establish a sufficient condition for the existence of a mild solution for a nonlinear fractional integro-differential equation with infinite time delay. The fractional derivative is considered in the sense of Caputo of order \(q\in (0,1)\). The argument is based on the fixed point theorem.

Reviewer: Roman Šimon Hilscher (Brno)

MSC:

26A33	Fractional derivatives and integrals
34G20	Nonlinear differential equations in abstract spaces
34K30	Functional-differential equations in abstract spaces
34K37	Functional-differential equations with fractional derivatives

Keywords:

semilinear differential equations; Caputo fractional derivative; mild solution; measure of noncompactness; fixed point; semigroup; Banach space