  We discuss spherically symmetric dynamical systems in the framework of a
general model of $f({\cal R})$ gravity, i.e. $f({\cal R})={\cal R}e^{\zeta
{\cal R}}$, where $\zeta$ is a dimensional quantity in squared length units
[L$^2$]. We initially assume that the internal structure of such systems is
governed by the Krori-Barua ansatz, alongside the presence of fluid anisotropy.
By employing astrophysical observations obtained from the pulsar {\textit SAX
J1748.9-2021}, derived from bursting X-ray binaries located within globular
clusters, we determine that $\zeta$ is approximately equal to $\pm 5$ km$^2$.
In particular, the model can create a stable configuration for {\textit SAX
J1748.9-2021}, encompassing its geometric and physical characteristics. In
$f({\cal R})$ gravity, the Krori-Barua approach links $p_r$ and $p_t$, which
represent the components of the pressures, to ($\rho$), representing the
density, semi-analytically. These relations are described as $p_r\approx v_r^2
(\rho-\rho_{I})$ and $p_t\approx v_t^2 (\rho-\rho_{II})$. Here, the expression
$v_r$ and $v_t$ represent the radial and tangential sound speeds, respectively.
Meanwhile, $\rho_I$ pertains to the surface density and $\rho_{II}$ is derived
using the parameters of the model. Notably, within the frame of $f({\cal R})$
gravity where $\zeta$ is negative, the maximum compactness, denoted as $C$, is
inherently limited to values that do not exceed the Buchdahl limit. This
contrasts with general relativity or with $f({\cal R})$ with positive $\zeta$,
where $C$ has the potential to reach the limit of the black hole
asymptotically. The predictions of such model suggest a central energy density
which largely exceeds the saturation of nuclear density, which has the value
$\rho_{\text{nuc}} = 3\times 10^{14}$ g/cm$^3$. Also, the density at the
surface $\rho_I$ surpasses $\rho_{\text{nuc}}$.
