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A calculation of the non-singlet part of spin dependent structure function,$xg_1^{NS}(x,Q^2)$ and associated sum rule, the Bjorken Sum rule up tonext-next-to-leading order(NNLO) is presented. We use a unified approachincorporating Regge theory and the theoretical framework of perturbativeQuantum Chromodynamics. Using a Regge behaved model with $Q^2$ dependentintercept as the initial input, we have solved theDokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equation up toNNLO at small-$x$ for $xg_1^{NS}(x,Q^2)$ and the solutions are utilised tocalculate the polarised Bjorken sum rule(BSR). We have also extracted thehigher twist contribution to BSR based on a simple parametrisation. Theseresults for both of $xg_1^{NS}(x,Q^2)$ and BSR, along with higher twistcorrections are observed to be consistent with the available data taken fromSMC, E143, HERMES, COMPASS and JLab experiments. In addition, our results arealso compared with that of other theoretical and phenomenological analysisbased on different models and a very good agreement is also observed in thisregard. Further a very good consistency between our calculated results andtheoretical QCD predictions of BSR is also achieved.

Small-x behavior of non-singlet spin structure function and Bjorken sum rule with pQCD correction up to NNLO and Higher twist correction