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Existence of mild solutions to fractional integrodifferential equations of neutral type with infinite delay. (English) Zbl 1213.45008
Summary: We study the solvability of the fractional integrodifferential equations of neutral type with infinite delay in a Banach space \(X\). An existence result of mild solutions to such problems is obtained under the conditions in respect of Kuratowski’s measure of noncompactness. As an application of the abstract result, we show the existence of solutions for an integrodifferential equation.

MSC:
45J05 Integro-ordinary differential equations
34A08 Fractional ordinary differential equations and fractional differential inclusions
45N05 Abstract integral equations, integral equations in abstract spaces
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