Aslantas, MustafaBachay, Ali HusseinSahin, HakanTurkoglu, A. Duran2026-02-082026-02-0820252473-6988https://doi.org/10.3934/math.2025854https://hdl.handle.net/20.500.12885/6105In this paper, we present two new concepts, called alpha-psi-iterated function system and alpha-psi proximal iterated function system, by using alpha-psi-contractions and alpha-psi-proximal contractions. Hence, we extended and generalized some definitions existing in the literature. We present some results that determine the necessary conditions to obtain a fractal with an attractor in the mentioned systems. Finally, some interesting examples are presented to apply our results.eninfo:eu-repo/semantics/openAccessiterated function systemsfractalsbest proximity pointArticle10.3934/math.20258541081910619125WOS:0015584235000022-s2.0-105015072471Q1Q1