Existence and uniqueness for a kind of nonlocal fractional evolution equations on the unbounded interval

By means of a Laplace transform and its inverse transform, we obtain a correct equivalent integral equation for some kind of nonlocal abstract differential equations (fractional order) on the right half-axis. Based on it, the existence result is established by Knaster’s theorem, and the uniqueness of the mild solution is obtained using the Banach contraction principle.