Vahid Sadri - Department of Mathematics, Shabestar Branch, Islamic Azad University Shabestar, Iran.
Reza Ahmadi - Institute of Fundamental Sciences, University of Tabriz, Tabriz, Iran.
Mohammad Jafarizadeh - Faculty of Physic, University of Tabriz, Tabriz, Iran.
Susan Nami - Faculty of Physic, University of Tabriz, Tabriz, Iran.

The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames  which is important for frame applications, have been specified  completely for the continuous frames. After improving and extending the concept of fusion frames and continuous frames, in this paper we introduce continuous $k$-fusion frames in Hilbert spaces. Similarly to the c-fusion frames, dual of continuous $k$-fusion frames may not be defined, we however define the $Q$-dual of continuous $k$-fusion frames. Also some new results and the perturbation of continuous $k$-fusion frames will be presented.

Fusion frame, $k$-fusion frame, c$k$-fusion frame, Q-duality