  In this work, we study the evolution of a fractal universe composed of
Tsallis holographic dark energy (THDE) and a pressureless dark matter that
interact with each other through a mutual interaction. We then reconstruct the
interaction term of this model by considering the Hubble length as the IR
cut-off scale. We also study the behavior of different cosmological parameters
during the cosmic evolution from the early matter-dominated era until the
late-time acceleration. The present study shows that the universe undergoes a
smooth transition from a decelerated to an accelerated phase of expansion in
the recent past. Moreover, we also shown the evolution of the normalized Hubble
parameter for our model and compared that with the latest cosmic chronometer
data. Finally, we test the viability of the model by exploring its stability
against small perturbation by using the squared of the sound speed.
