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

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