This paper is devoted to study the possibility of forming anisotropic compact stars in modified Gauss-Bonnet, namely called as f (G) theory of gravity which is one of the strong candidates, responsible for the accelerated expansion of the universe. For this purpose, we have used analytical solution of Krori and Barua metric to the Einstein field equations with anisotropic form of matter and power law model of f (G) gravity. To determine the unknown constants in Krori and Barua metric, we have used the sample of compact stars, 4U 1820-30, Her X-1, SAX J 1808-3658. The physical behavior of these stars have been analyzed with the observational data. In this setting, we have checked all the regularity conditions and stability of the compact stars 4U 1820-30, Her X-1, SAX J 1808-3658.

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This paper deals with the new theoretical model of quintessence anisotropic star in f (T ) theory of gravity. The equations of motion in f (T ) theory with a static spherically symmetric spacetime in the presence of anisotropic fluid and quintessence field have been solved by using KroriBarua metric. In this case, we have used the diagonal tetrad field that leads to a linear form f (T ) function. We have determined that all the obtained solutions are free from central singularity and potentially stable. The values of the unknown constants existing in Krori and Barua metric have been calculated by using the observed values for mass of the different strange stars PSR J 1614-2230, SAXJ1808.4-3658(SS1), 4U1820-30, PSR J 1614-2230. The physical parameters (anisotropy, stability and redshift) of the stars have been investigated in detail. We have determined the constraint under which results of f (T ), theory reduces to general relativity.

In this article, the authors have discussed a new exact model of anisotropic stars in the f(T) theory of gravity. A parametric form of the metric functions has been implemented to solve the dynamical equations in f(T) theory with the anisotropic fluid. The novelty of the work is that the obtained solutions do not contain singularity but are potentially stable. The estimated values for mass and radius of the different strange stars, RX J 1856–37, Her X-1, and Vela X-12, have been utilized to find the values of unknown constants in Krori and Barua metrics. The physical parameters like anisotropy, stability, and redshift of the stars have been examined in detail.

In this paper, certain Hermite–Jensen–Mercer type inequalities are proved via conformable integrals of arbitrary order. We establish some different and new fractional Hermite–Hadamard–Mercer type inequalities for a differentiable function f whose derivatives in the absolute values are convex.