This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of fractional integrals. The approach seamlessly aligns with established techniques used in addressing problems involving integer-order operators, contributing to a unified framework for numerical solutions.

翻译：本研究重新审视了分数阶积分的扩散表示，旨在开创此类表示的新变体。这些变体旨在为分数阶积分的近似计算提供高效的数值算法。该方法与处理整数阶算子问题的已有技术无缝衔接，有助于构建统一的数值求解框架。