带有非奇异核分数阶差分方程的比较原理及解的不确定性分布

A Comparison Theorem and the Uncertainty Distribution of Solutions for Fractional Difference Equations with Nonsingular Kernel

比较原理对于研究分数阶方程的性质具有重要的作用。首先,证明了ABR型分数阶差分方程的比较原理。其次,利用比较原理,建立了不确定性分数阶差分方程的解与其α-路径之间的联系。接着,给出了ABR型不确定性分数阶差分方程解的不确定性分布。最后,具体的实例验证了主要结论的正确性。

Comparison theorems play an essential role in studying the properties of the fractional equations. Firstly, a comparison theorem for ABR type fractional difference equations is proved. Next, based on the proven comparison theorem, the connections between the solution for an uncertainty fractional difference equation and its α-path are established. Then, the uncertainty distribution of solutions for ABR type uncertainty fractional difference equations is also derived. Finally, examples are given to verify the correctness of main results.