  In this work, we consider a number of boundary-value problems for
time-fractional heat equation with the recently introduced Caputo-Fabrizio
derivative. Using the method of separation of variables, we prove a unique
solvability of the stated problems. Moreover, we have found an explicit
solution to certain initial value problem for Caputo-Fabrizio fractional order
differential equation by reducing the problem to a Volterra integral equation.
Different forms of solution were presented depending on the values of the
parameter appeared in the problem.
