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This paper is concerned with the existence of mild solutions for fractional semilinear differential equations with non local conditions in separable Banach spaces. The result is established by using the technique of measures of noncompactness in Banach spaces of continuous functions and Schauder fixed point theorem. (2010): 34G20, 35R10. Mathematics subject classification

In this paper, we study the existence of mild solutions for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators generating compact semigroup on the Banach space. The arguments are based on the Schauder fixed point theorem