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In this paper, we present {\tt SMKA18} analysis which is a first attempt toextract the set of next-to-next-leading-order (NNLO) spin-dependent partondistribution functions (spin-dependent PDFs) and their uncertainties determinedthrough the Laplace transform technique and Jacobi polynomial approach. Usingthe Laplace transformations, we present an analytical solution for thespin-dependent Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution equationsat NNLO approximation. The results are extracted using 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 recenthigh-precision measurements from {\tt COMPASS16} experiments at CERN which areplaying an increasingly important role in global spin-dependent fits. Thecareful estimations of uncertainties have been done using the standard 'Hessianerror' propagation. We will compare our results with the availablespin-dependent inclusive deep inelastic scattering dataset and other resultsfor the spin-dependent PDFs in literature. The results obtained for thespin-dependent PDFs as well as spin-dependent structure functions are clearlyexplained both in the small and large values of $x$.

Analytical approaches to the determination of spin-dependent parton distribution functions at NNLO approximation