We consider a nonflat Friedmann–Robertson–Walker universe filled by a pressureless dark matter and Tsallis holographic dark energy (THDE) whose IR cutoff is the apparent horizon.We also consider both noninteracting and interacting cases in which a mutual interaction between the two dark sectors of cosmos is taken into account. For the noninteracting case, the density, equation of state (EoS) and the deceleration parameters show a satisfactory behavior by themselves, and the phantom line is not crossed. In this manner, unlike the flat case for THDE (Tavayef et al. in Phys Lett B 781:195, 2018), where the squared of sound speed is always negative, the squared of sound speed is negative and approaches zero at future. In the interacting case, the phantom line is crossed by EoS parameter, the squared of the sound speed is always negative and the density and deceleration parameters have acceptable behavior. Finally, by studying the thermodynamic parameters, namely the heat capacities and the compressibility criterions, the thermal stability of both cases are discussed which reveals that both models are thermodynamically unstable.
