This paper proposes the study of a newer class of integro-differential operators, which allow analysing a more general family of dynamical systems, with not necessarily integer-order differentiable solutions, and based on Volterra integral equations of the second kind. One of the main advantages of the present study is that the proposed operators include, in particular cases, some classical and modern formulations of fractional- and distributed-order derivatives. In contrast to conventional methodologies, the integer-order differentiability of the solution is not assumed, allowing to deem on a more general class of dynamical systems and non-smooth techniques for robust stabilisation. The formal presentation of novel tools could result in high interest for robust control of more varied dynamical processes. Representative simulations are also presented in order to highlight the feasibility of the proposed methods.

本文建议研究一类较新的积分微分算子，它允许分析更一般的动力系统族，不一定是整数阶可微解，并基于第二类 Volterra 积分方程。本研究的主要优点之一是所提出的算子在特定情况下包括分数阶和分布式阶导数的一些经典和现代公式。与传统方法相比，不假设解的整数阶可微性，允许将更一般的动态系统和非光滑技术视为鲁棒稳定。新工具的正式展示可能会引起人们对更多样化的动态过程的稳健控制的高度兴趣。