We explore the effects of considering various infrared (IR) cutoffs, including the particle horizon, the Ricci horizon and the Granda–Oliveros (GO) cutoffs, on the properties of Tsallis holographic dark energy (THDE) model, proposed inspired by Tsallis generalized entropy formalism (Tavayef et al. in Phys Lett B 781:195, 2018). Interestingly enough, we find that for the particle horizon as IR cutoff, the obtained THDE model can describe the late time accelerated universe. This is in contrast to the usual HDE model which cannot lead to an accelerated universe, if one considers the particle horizon as the IR cutoff.We also investigate the cosmological consequences of THDE under the assumption of a mutual interaction between the dark sectors of the Universe. It is shown that the evolution history of the Universe can be described by these IR cutoffs and thus the current cosmic acceleration can also be realized. The sound instability of the THDE models for each cutoff are also explored, separately.
