Abstract: By using operator semigroup theory and upper and lower solution monotone iterative methods, we discuss the existence of mild solutions to  initial value problems for a class of Conformable fractional evolution equations  with Volterra-type integral operators in Banach spaces, where T_α represents the  Conformable fractional derivative operator with order 0<α<1, A is a coherently closed linear operator. Under the condition that the nonlinear term satisfies the appropriate inequality, the existence of the mild solution to the equation is obtained.

Key words: fractional evolution equation, mild solution, upper and lower solution, monotone iterative method