  In this article, we obtain higher H\"older regularity results for weak
solutions to nonlocal problems driven by the fractional double phase operator
  \begin{align*}
  \mc L u(x):=&2 \; {\rm P.V.} \int_{\mathbb R^N}
\frac{|u(x)-u(y)|^{p-2}(u(x)-u(y))}{|x-y|^{N+ps_1}}dy \nonumber
  &+2 \; {\rm P.V.} \int_{\mathbb R^N} a(x,y)
\frac{|u(x)-u(y)|^{q-2}(u(x)-u(y))}{|x-y|^{N+qs_2}}dy,
  \end{align*}
  where $1<p\leq q<\infty$, $0<s_2, s_1<1$ and the modulating coefficient
$a(\cdot,\cdot)$ is a non-negative bounded function. Specifically, we prove
higher space-time H\"older continuity result for weak solutions of time
depending nonlocal double phase problems for a particular subclass of the
modulating coefficients. Using suitable approximation arguments, we further
establish higher (global) H\"older continuity results for weak solutions to the
stationary problems involving the operator $\mc L$ with modulating coefficients
that are locally continuous.
