In this paper, we study two di®erent dynamic structures of holographic dark energy, namely Tsallis and Kaniadakis, within the framework of Brans{Dicke cosmology. We consider the complex form of the quintessence model and examine both non-interacting and interacting cases, calculating various cosmological parameters such as the equation of state ! and discussing the behavior of ! !0. We modify the potential and study the scalar ¯eld dynamics of complex quintessence cosmology. Additionally, we examine the e®ects of the two parts of the quintessence ¯eld (real and complex) and the fractional energy density D, determining whether they can describe a real universe. We note that the fractional energy density cannot be arbitrary between 0 and 1, as it depends on the Tsallis, Kaniadakis and Brans{Dicke cosmology-free parameters. For each model, we establish a relationship between the fractional energy density and other parameters such as , b2, and .
