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Based on an equivalent integral equation of a new type for a class of fractional evolution equations, which is different from those obtained in the existing literature, the paper investigates a class of fractional evolution equations with nonlocal conditions on infinite interval. Without the assumption of lower and upper solutions, we present a new result on the existence and uniqueness of positive mild solutions for the abstract fractional evolution equations by using the monotone iterative method.

Existence and uniqueness of positive mild solutions for a class of fractional evolution equations on infinite interval