Interior and boundary regularity results for strongly nonhomogeneous p, q-fractional problems

In this article, we deal with the global regularity of weak solutions to a class of problems involving the fractional (p, q)-Laplacian, denoted by (-Delta)(p)(s1) + (-Delta)(q)(s2) for s(2), s(1) is an element of (0, 1) and 1 < p, q < infinity. We establish completely new Holder continuity results, up to the boundary, for the weak solutions to fractional ( p, q)-problems involving singular as well as regular nonlinearities. Moreover, as applications to boundary estimates, we establish a new Hopf-type maximum principle and a strong comparison principle in both situations.