A Picard type theorem concerning meromorphic functions of\\ hyper-order

Let $f(z)$ be a meromorphic function in the complex plane, whose poles are multiple and whose zeros have multiplicity at least $3$. Set $\alpha(z):=\beta(z)\exp{(\gamma(z))}$, where $\beta(z)$ is a nonconstant elliptic function and $\gamma(z)$ is an entire function. In this paper, we prove that if $\sigma(f(z))>\sigma(\alpha(z))$, then $f'(z)=\alpha(z)$ has infinitely many solutions.