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The present study explores the    $$f(\mathcal {R},\mathcal {T})$$    f  (  R  ,  T  )modified gravity on the basis of observational data for three different compact stars with matter profile as anisotropic fluid without electric charge. In this respect, we adopt the well-known Karmarker condition and assume a specific and interesting model for    $$\mathrm {g}_{rr}$$    g   rrmetric potential component which is compatible with this condition. This choice further leads to a viable form of metric component    $$\mathrm {g}_{tt}$$    g   ttby utilizing the Karmarkar condition. We also present the interior geometry in the reference of Schwarzschild interior and Kohler–Chao cosmological like solutions for    $$f(\mathcal {R},\mathcal {T})$$    f  (  R  ,  T  )theory. Moreover, we calculate the spacetime constants by using the masses and radii from the observational data of three different compact stars namely 4U 1538-52, LMC X-4 and PSR J1614-2230. In order to explore the viability and stability of the obtained solutions, some physical parameters and properties are presented graphically for all three different compact object models. It is noticed that the parameters  c  and    $$\lambda $$   λhave some important and considerable role for these solutions. It is concluded that our obtained solutions are physically acceptable, bearing a well-behave nature in    $$f(\mathcal {R},\mathcal {T})$$    f  (  R  ,  T  )modified gravity.

Realistic stellar anisotropic model satisfying Karmarker condition in f(R, T) gravity