The aim of this paper is to obtain some new Hermite-Hadamard type of inequalities via harmonic convex, strongly harmonic convex, strongly harmonic log-convex functions, and AH-convex in connection with quantum calculus. All the results reduce to ordinary calculus case when q → 1 − .

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In this work, a modified viscoelastic model of initially stressed microbeam on the base of the Winkler foundation under the effect of ultrafast laser heating and axial stress has been proposed. Viscosity effects are taken into account following the Kelvin–Voigt model. The governing equation for the thermoelastic vibration of the microbeam is obtained when the thermal field effect is defined by the non-Fourier Moore–Gibson–Thompson (MGT) heat equation. The microbeam is seen as an Euler–Bernoulli beam that is exposed to varying sinusoidal heat. An analytical solution to the problem has been presented on the basis of the Laplace transform in addition to applying a numerical method to find inverse transformations. A numerical illustration is organized in the discussion section which discusses the impact of different effective parameters both on the vibrational behavior of a microbeam system and on the field variables. The viscous damping coefficient, laser pulse duration, and axial load greatly affect the deflection and temperature responses. The results obtained are verified and compared with the literature.

The idea of this paper is to look some anisotropic star models in a metric approach, where R is the Ricci scalar. The Karmarkar and Tolman system is used to analyze the physics of some spherically symmetric stars using two independent computational gravitational theories. The behavior of structural factors is evaluated using diagrams, and the feasibility of compact objects is investigated using boundary conditions for the involved constants. The investigation in the profiles of the effective energy/matter states, the equilibrium phases, and the Tolman‐Oppenheimer‐Volkoff models and stability analysis is performed for various realistic candidates of stars. Under a few important cosmological backgrounds, the assessment of our graphics may offer assistance in the search of the realistic and viable gravitational models.

The major goal of this work is to find solutions of Einstein-Maxwell field equations for anisotropic, expansion-free, non-static, spherically distributed matter content. The analytical models that highlight the major benefit of simplicity are shown and this makes it possible to use them as a toy model to illustrate how cavities evolve. Furthermore, the transport equations, quasi-homologous constraints and the junction conditions are also evaluated along with its useful implications. Eventually, the consequences of electric force on this system are summed up in the last section.