  The Jeans instability is regarded as an important tool for analyzing the
dynamics of a self-gravitating system. However, this theory is challenging
since astronomical observation data show some Bok globules, whose masses are
less than the Jeans mass and still have stars or at least undergo the star
formation process. To explain this problem, we investigate the effects of the
higher-order generalized uncertainty principle on the Jeans mass of the
collapsing molecular cloud. The results in this paper show that the higher
order generalized uncertainty principle has a very significant effect on the
canonical energy and gravitational potential of idea gas, and finally leads to
a modified Jeans mass lower than the original case, which is conducive to the
generation of stars in small mass Bok globules. Furthermore, we estimate the
new generalized uncertainty principle parameter $\gamma _0$ by applying various
data of Bok globules, and find that the range of magnitude of $\gamma _0$ is
${10^{11}} \sim {10^{12}}$.
