$f(T,B)$ gravity in a Friedmann-Lema\^{\i}tre-Robertson-Walker universe with nonzero spatial curvature

We investigate exact solutions and the asymptotic dynamics for the Friedmann-Lema^{\i}tre-Robertson-Walker universe with nonzero spatial curvature in the fourth-order modified teleparallel gravitational theory known as $f(T,B)$ theory. We show that the field equations admit a minisuperspace description, and they can reproduce any exact form of the scale factor. Moreover, we calculate the equilibrium points and analyze their stability. We show that Milne and Milne-like solutions are supported, and the de Sitter universe is provided. To complete our analysis, we use Poincar'e variables to investigate the dynamics at infinity.