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This paper is concerned with  the existence of  mild solutions forthe fractional integrodifferential equations  with finite delay andalmost sectorial operators in a separable Banach space X. We obtain existence theorem for mild solutions to the above-mentioned equations, by means of measure of noncompactness and the resolvent operators associated with almost sectorial operators. As an application, the existence of mild solutions for some integrodifferential equation isobtained

Existence of the Mild Solutions for Delay Fractional Integrodifferential Equations with Almost Sectorial Operators