  The scenario of slow-roll inflation is explored in the $f(R,T)$ theory of
gravity where a non-minimal coupling between matter and curvature is included.
A noncanonical scalar field is assumed to play the role of inflaton which
contains generalized kinetic energy. The study is performed by taking the
Hamilton-Jacobi formalism where the Hubble parameter is taken as a function of
the scalar field. In this regard, a power-law function and an exponential
function of the scalar field are assumed for the Hubble parameter and the model
is considered in detail. By performing Python coding and applying the
observational data, the free parameters of the model are determined for which
the model is put in perfect consistency with the data. Then, using the results,
the validity of the swampland criteria and TCC is considered. It is realized
that not only the model comes to a good agreement with data, but it also could
satisfy the swampland criteria.
