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.

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