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In this paper, we investigate the dark energy phenomenon by studying theTsallis holographic dark energy within the framework of Brans-Dicke (BD)scalar-tensor theory of gravity [Phys. Rev. \textbf{124}, 925 (1961)]. In thiscontext, we choose the BD scalar field $\phi$ as a logarithmic function of theaverage scale factor $a(t)$ and Hubble horizon as the IR cutoff ($L=H^{-1}$).We reconstruct two cases of non-interacting and interacting fluid (dark sectorsof cosmos) scenario. The physical behavior of the models are discussed with thehelp of graphical representation to explore the accelerated expansion of theuniverse. Moreover, the stability of the models are checked through squaredsound speed $v_s^2$. The well-known cosmological plane i.e.,$\omega_{de}-\omega^{\prime}_{de}$ is constructed for our models. We alsoinclude comparison of our findings of these dynamical parameters withobservational constraints. It is also quite interesting to mention here thatthe results of deceleration, equation of state parameters and$\omega_{de}-\omega^{\prime}_{de}$ plane coincide with the modern observationaldata.

Observational constraint on interacting Tsallis holographic dark energy in logarithmic Brans-Dicke theory