  In this article, we establish the symmetric positive existence for the
following Caputo fractional boundary value problem \begin{align*}
{}^{C}D_{0}^{\,\mu}x(t)+f(t,x(t))&=0,\hspace{1cm}t\in(-1,\,1),\hspace{1cm}1<\mu\leq2,\\
x(\pm1)=x'(0^{\pm})&=0, \end{align*} where
${}^{C}D_{0}^{\,\mu}x(t)={}^{C}D_{0^{+}}^{\,\mu}x(t)$ for $t\geq0$,
${}^{C}D_{0}^{\,\mu}x(t)={}^{C}D_{0^{-}}^{\,\mu}x(t)$ for $t\leq0$. Moreover,
$f:(-1,\,1)\times(0,\infty)\rightarrow\mathbb{R}$ is continuous and singular at
$t=-1$, $t=1$ and $x=0$. Here, ${}^{C}D_{0^{+}}^{\,\mu}$ and
${}^{C}D_{0^{-}}^{\,\mu}$, respectively, are Caputo fractional left and right
derivatives of order $\mu$.
