| Summary: | The present paper reports a study on neutron stars in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity framework for the Hu–Sawicki model, Starobinsky model, Tsujikawa model, and Exponential Gravity model. First, we have used the TOV equation for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity framework, where we obtained two higher order differential equations for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>λ</mi></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ψ</mi></semantics></math></inline-formula>, with both functions depending on the radial coordinate. Furthermore, we have considered the BD theory, which is an equivalent theory of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>R</mi><mo>)</mo></mrow></semantics></math></inline-formula> gravity, and introduced a new scalar field <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>ϕ</mi><mn>2</mn></msub></semantics></math></inline-formula> with the scalar potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><msub><mi>ϕ</mi><mn>2</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>. We have observed an increase in the scalar potential with respect to <i>R</i> in each case. Furthermore, our proposed models, namely quadratic form, exponential form, and linear form and the other viable models show a similar type of evolution for the scalar potential <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>V</mi><mo>(</mo><msub><mi>ϕ</mi><mn>2</mn></msub><mo>)</mo></mrow></semantics></math></inline-formula>.
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