  We study inverse problems for semilinear elliptic equations with fractional
power type nonlinearities. Our arguments are based on the higher order
linearization method, which helps us to solve inverse problems for certain
nonlinear equations in cases where the solution for a corresponding linear
equation is not known. By using a fractional order adaptation of this method,
we show that the results of [LLLS20a, LLLS20b] remain valid for general power
type nonlinearities.
