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

##### 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
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