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In this paper, we present ``{\tt SMKA18}'' which is the first set of next-to-next-leading-order (NNLO) spin-dependent parton distribution functions (spin-dependent PDFs) and their uncertainties determined through the Laplace transform technique and Jacobi polynomial approach.
Using the Laplace transformations, we present an analytical solution for the spin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations at NNLO approximation. The results shown made use of a wide range of proton $g_1^{p}(x, Q^2)$, neutron $g_1^{n}(x, Q^2)$ and deuteron $g_1^{d}(x, Q^2)$ spin-dependent structure functions dataset including the most recent high-precision measurements from {\tt COMPASS16} experiments at CERN which are playing an increasingly important role in global spin-dependent fits. The careful estimations of uncertainties have been performed using the standard ``Hessian error'' propagation. We compare our results with the available spin-dependent inclusive DIS dataset and other results for the spin-dependent PDFs in literature. The obtained results for the spin-dependent PDFs as well as spin-dependent structure functions are clearly explained both in the small and large values of $x$.
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