  This article concerns with the global H\"older regularity of weak solutions
to a class of problems involving the fractional $(p,q)$-Laplacian, denoted by
$(-\Delta)^{s_1}_{p}+(-\Delta)^{s_2}_{q}$, for $1<p,q<\infty$ and $s_1,s_2\in
(0,1)$. We use a suitable Caccioppoli inequality and local boundedness result
in order to prove the weak Harnack type inequality. Consequently, by employing
a suitable iteration process, we establish the interior H\"older regularity for
local weak solutions, which need not be assumed bounded. The global H\"older
regularity result we prove expands and improves the regularity results of
Giacomoni, Kumar and Sreenadh (arXiv: 2102.06080) to the subquadratic case
(that is, $q<2$) and more general right hand side, which requires a different
and new approach. Moreover, we establish a nonlocal Harnack type inequality for
weak solutions, which is of independent interest.
