This paper primarily focuses on the distributions of the solutions for uncertain fractional difference equations by comparison theorems. First, comparison theorems are obtained for the fractional difference equations involving Riemann–Liouville type. Then the concepts of symmetrical uncertain variable and $\alpha$-path to an uncertain fractional difference equation are introduced. Moreover, the relations between the solutions for the uncertain fractional difference equations with symmetrical uncertain variables and their $\alpha$-paths are established and verified by the obtained comparison theorems. Finally, the numerical results of the uncertainty distributions of solutions for the uncertain fractional difference equations are proposed, considering the relations between their solutions and $\alpha$-paths.

本文主要通过比较定理着眼于不确定分数差方程的解的分布。首先，针对涉及Riemann–Liouville型的分数差分方程，获得比较定理。然后是对称不确定变量和$\alpha$引入了不确定的分数差分方程的路径。此外，具有对称不确定变量的不确定分数阶差分方程的解及其之间的关系$\alpha$建立路径并通过获得的比较定理进行验证。最后，考虑了它们之间的关系，提出了不确定分数差分方程解的不确定性分布的数值结果。$\alpha$-路径。