  In this paper, we establish a generalization of Sturm--Picone comparison
theorem for a pair of fractional nonlocal equations: \begin{eqnarray*}
  \begin{gathered}
  (-div. (A_1(x)\nabla))^{s} u = C_{1}(x) u \,\,\,\mbox{in}\,\,\Omega,
  u = 0 \,\,\,\,\mbox{on}\,\,\,\,\,\,\,\partial \Omega, \end{gathered}
  \end{eqnarray*} and
  \begin{eqnarray*}
  \begin{gathered}
  (-div. (A_2(x)\nabla))^{s} v = C_{2}(x) v \,\,\,\mbox{in}\,\,\Omega,
  v = 0 \,\,\,\,\mbox{on}\,\,\,\,\,\,\,\partial \Omega, \end{gathered}
  \end{eqnarray*} where $\Omega\subset \mathbb{R}^n$ is an open bounded subset
with smooth boundary, $0<s<1,\,\,A_1,\,A_2$ are real symmetric and positive
definite matrices on $\Omega$ with continuous entries on $\overline{\Omega}$
and $C_{1}, C_{2}\in C(\overline{\Omega}).$
