In this paper, new forms of nano continuous functions in terms of the notion of
nano Iα-open sets called nano Iα-continuous functions, strongly nano Iα-continuous
functions and nano Iα-irresolute functions will be introduced and studied. We
establish new types of nano Iα-open functions, nano Iα-closed functions and nano
Iα-homeomorphisms. A comparison between these types of functions and other
forms of continuity will be discussed. We prove the isomorphism between simple
graphs via the nano continuity between them. Finally, we apply these topological
results on some models for medicine and physics which will be used to give a
solution for some real-life problems.