Meromorphic functions of finite $\phi$-order and linear Askey-Wilson divided difference equations

The growth of meromorphic solutions of linear difference equations containing Askey-Wilson divided difference operators is estimated. The $\phi$-order is used as a general growth indicator, which covers the growth spectrum between the logarithmic order ${\rho }_{\log }(f)$ and the classical order $\rho (f)$ of a meromorphic function $f$.