Sharp Bounds for Trigonometric and Hyperbolic Functions with Application to Fractional Calculus

Abstract

Sharp bounds (Formula presented) were obtained, as well as one new bound for (Formula presented) A new situation to note about the obtained boundaries is the symmetry in the upper and lower boundary, where the upper boundary differs by a constant from the lower boundary. New consequences of the inequalities were obtained in terms of the Riemann–Liovuille fractional integral and in terms of the standard integral.