The authors study the functional differential equation with retarded argument having the form
where denotes the fractional derivative. Moreover, the functional integral equation of fractional order of the form
is also investigated. In (2) it is assumed that satisfies the classical Carathéodory conditions and is a member of the space . A few theorems on the existence of solutions of (1) and (2) are established. Some results concerning the existence of the extremal solutions and comparison type theorems concerning (2) are also derived.