In this research article, we investigate reverse Radon's inequality, Bergström's the weighted power mean Schlömilch's Bernoulli's inequality and Lyapunov's with Specht's ratio on time scales. We also present Rogers--Holder's logarithmic The scale dynamic inequalities unify extend some continuous their corresponding discrete quantum versions.

in this research, the bending analysis of rectangular nanoplates subjected to mechanical loading is investigated. for this purpose, the strain gradient elasticity theory with one gradient parameter is presented to study the nanoplates. from the best knowledge of authors, it is the first time that the exponential shear deformation formulation based on strain gradient elasticity theory is carried...