Tsallis holographic dark energy model with event horizon cutoff in modified gravity

In this paper, we considered the Tsallis holographic dark energy model in frames of Nojiri-Odintsov gravity with f(R) = R + lambda R-2 - sigma mu/R. For IR, cutoff event horizon is taken. The cosmological evolution of such universe is investigated for various initial conditions and values of parameters. The dependence of the Hubble parameter H from time in the future has an oscillation. It is shown that for mu not equal 0 appearance of singularities are typical and the time up to these singularities can be relatively small from cosmological viewpoint. The singularity is associated with the zero of second derivative of f(R) on R. It is interesting to note that these models can describe observational data from Ia supernovae astrophysics and dependence of the Hubble parameter from redshift z at least not worse than canonical Lambda CDM model.