  We consider $f(R,T)$ modified theories of gravity in the context of string
theory inspired dilaton gravity. We deal with a specific model that under
certain conditions describes the late time Universe in accord with
observational data in modern cosmology and addresses the $H_0$ tension. This is
done by exploring the space of parameters made out of those coming from the
modified gravity and dilatonic charge sectors. We employ numerical methods to
obtain several important observable quantities.
