In this article, we communicate with the glimpse of the proofs of new global regularity results for weak solutions to a class of problems involving fractional (p,q)-Laplacian, denoted by (−∆)_p$^{s1}$ + (−∆)_q$^{s2}$ , for s₂, s₁ ∈ (0,1) and 1 < p,q < ∞. We also obtain the boundary Hölder continuity results for the weak solutions to the corresponding problems involving at most critical growth nonlinearities. These results are almost optimal. Moreover, we establish Hopf type maximum principle and strong comparison principle. As an application to these new results, we prove the Sobolev versus Hölder minimizer type result, which provides the multiplicity of solutions in the spirit of seminal work