Stability analysis of a class of integral equations with not necessarily differentiable solutions

Abstract 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.