Stability analysis of anisotropic stellar structures in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si3.svg" display="inline" id="d1e408"><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

The article explores the dynamics and stability of compact stars in the field of f(R) gravity by investigating the empirical data of different significant compact star candidates. We used the corrections offered by Karmarkar and Tolman to examine the properties of these specific compact stars. For different values of the curvature term, we analyzed the behavior of material variables, energy conditions, equations of state parameters, anisotropy measurements, and the Tolman–Oppenheimer–Volkoff equation in the modeling of stellar structures We provided illustrations with their graphical representations that depict the configuration of the compact stars. For this purpose, we utilized known f(R)-gravity models to express these results as graphical representations to provide evidence supporting the authenticity and stability of the stars.

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