In this paper the existence of unique positive solutions for system of $(p,q,r)$-Laplacian Sturm–Liouville type two-point fractional order boundary value problems,
\[
C_{0^{+}}^{\alpha}(\phi_{p}(u(t))) + f(t, u(t), v(t), w(t)) = 0, \quad 0 < t < 1,
\]
\[
C_{0^{+}}^{\beta}(\phi_{q}(v(t))) + g(t, v(t), w(t), u(t)) = 0, \quad 0 < t < 1,
\]
\[
C_{0^{+}}^{\gamma}(\phi_{r}(w(t))) + h(t, w(t), u(t), v(t)) = 0, \quad 0 < t < 1,
\]
\[
a_{1}(\phi_{p}u)(0) – b_{1}(\phi_{p}u)'(0) = 0, \quad c_{1}(\phi_{p}u)(1) + d_{1}(\phi_{p}u)'(1) = 0,
\]
\[
a_{2}(\phi_{q}v)(0) – b_{2}(\phi_{q}v)'(0) = 0, \quad c_{2}(\phi_{q}v)(1) + d_{2}(\phi_{q}v)'(1) = 0,
\]
\[
a_{3}(\phi_{r}w)(0) – b_{3}(\phi_{r}w)'(0) = 0, \quad c_{3}(\phi_{r}w)(1) + d_{3}(\phi_{r}w)'(1) = 0,
\]
where $1 < \alpha, \beta, \gamma \le 2$, $\varphi(\tau) = |\tau|^{\ell-2}\tau$, $\ell \in (1, \infty)$, $C_{0^{+}}^{\ast}$ is a Caputo fractional derivative of order $\ast \in \{\alpha, \beta, \gamma\}$ and $a_i, b_i, c_i, d_i$, $i = 1,2,3$, are positive constants, is established by an application of $n$-fixed point theorem of ternary operators on partially ordered metric spaces.