  The purpose of this paper is to study the Tsallis agegraphic dark energy with
an interaction term between dark energy and dark matter in the DGP brane-world
scenario. For this, we assume some initial conditions to obtain the dark energy
density, deceleration, dark energy EoS, and total EoS parameters. Then, we
analyze the statefinder parameters, $\omega'{}_{DE}-\omega_{DE}$ plots, and
classical stability features of the model. The results state that the
deceleration parameter provides the phase transition from decelerated to
accelerated phase. The $\omega_{DE}$ graphs show the phantom behavior, while
the $\omega_{tot}$ exhibits the quintessence and phantom during the evolution
of the Universe. Following the graphs, the Statefinder analysis shows the
quintessence behavior of the model for the past and present. However, it tends
to the $\Lambda CDM$ in the following era. The $\omega'{}_{DE}-\omega_{DE}$
plot indicates the thawing or freezing area depending on the type of era and
different values of $b^{2}$, $\delta$, and $m$. By the square of the sound
speed, we see the model is stable in the past, stable or unstable at the
current time, and unstable in the future for selected values of $b^{2}$,
$\delta$, and $m$. To test the model, we use the recent Hubble data. We also
employ Akaike Information Criterion (AIC) and Bayesian Information Criterion
(BIC) to compare the model with the $\Lambda CDM$ as the reference model. In
addition, we test the model using the $H-z$ plot, and we see a turning point in
the future time. The results from the best fit values for the $\omega_{tot}$
plot emphasize that the Universe is in the quintessence region in the current
time. It will enter the phantom phase, and then it will approach the $\Lambda$
state in the future. But, the $\omega_{DE}$ always stays on the phantom region.
The model is unstable in the present and progressive era.
