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Of concern is the existence of mild solutions to delay fractional differential equations with almost sectorial operators. Combining the techniques of operator semigroup, noncompact measures and fixed point theory, we obtain a new existence theorem without the assumptions that the nonlinearity f satisfies a Lipschitz-type condition, and the resolvent operator associated with A is compact. An example is presented.

Mild solutions for abstract fractional differential equations with almost sectorial operators and infinite delay