A note on deranged Bell polynomials and numbers

Abstract In this paper, we introduce the deranged Bell polynomials as a natural generalization of the deranged Bell numbers defined by Belbachir et al. and investigate several of their interesting properties. Moreover, using umbral calculus, we express these polynomials as linear combinations of Bernoulli, Euler, Changhee, Daehee, and Bell polynomials, thereby revealing their interrelationships.