Embedded class-I solution of compact stars in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e884" altimg="si260.svg"><mml:mrow><mml:mi>f</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>R</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math> gravity with Karmarkar condition

This paper's main aim is to investigate the existence of a new classification embedded class-I solutions compact stars, by using Karmarkar condition in $f(R)$ gravity background. To achieve that goal, we consider two different models theory for static spherically symmetric spacetime considering anisotropic matter distribution. Further, employ relate components metric potentials $g_{rr}$ and $g_{tt}$. We assume particular model one potential obtain second condition. Moreover, also calculate values constant parameters observational data these namely, $Vela~ X-1,$ $PSR~J1614-2230,$ $4U~1608-52,$ $Cen~X-3$ $4U~1820-30.$ perform physical tests like variational behavior energy density pressure components, stability equilibrium conditions, constraints, mass function adiabatic index check viability models. All attributes indicate consistent our Our investigation suggests appears as suitable describing objects.