  In this paper, the Schwarz type and Schwarz-Pick type inequalities for
solutions of $\alpha$-harmonic equation for $\alpha>-1$ are investigated. By
making use of the integral of trigonometric functions, we obtain the two types
of inequalities in terms of hypergeometric functions which improve the
corresponding results due to Khalfallah et al. (Complex Var. Elliptic Equ.,
2023) and Li et al. (Bull. Malays. Math. Sci. Soc., 2022).
