In this paper, we consider some generalization of the Banach contraction principle, namely cyclic contraction and cyclic φ-contraction. For the application to the fractal, we develop new iterated function systems (IFS) consisting of cyclic contractions and cyclic φ-contractions. Further, we discuss about some special properties of the Hutchinson operator associated with the cyclic (c)-comparison IFS. © 2020, Springer Nature Switzerland AG.