We study the solutions of the fractional differential equation \begin{equation*} ^{LC}D_{z}^{lpha }f^{rime }(z)+A(z)^{LC}D_{z}^{\beta }f(z)+B(z)f(z)=0 \end{equation*} where $^{LC}D_{z}^{\alpha }$ and $^{LC}D_{z}^{\beta }$ are the Liouville-Caputo fractional derivatives of orders $n-1 \lt \alpha, \beta \leq n \in \mathbb{N}^{\ast}$, and $z$ is complex number, $A(z),B(z)$ be entire functions. We find conditions on the coefficients so that every solution that is not identically zero has infinite order.