# Controlled Singular Volterra Integral Equations and Pontryagin Maximum Principle

arXiv: https://arxiv.org/abs/1712.05911 · HTML: https://mlsanity.com/paper/1712.05911/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Dec 2017.

## Built on by (most cited first, 1 of 1)

- [Dynamical Survival Analysis with Controlled Latent States](https://mlsanity.com/paper/2401.17077/) (2024)

## Abstract (arXiv)

This paper is concerned with a class of controlled singular Volterra integral equations, which could be used to describe problems involving memories. The well-known fractional order ordinary differential equations of the Riemann--Liouville or Caputo types are strictly special cases of the equations studied in this paper. Well-posedness and some regularity results in proper spaces are established for such kind of questions. For the associated optimal control problem, by using a Liapounoff's type theorem and the spike variation technique, we establish a Pontryagin's type maximum principle for optimal controls. Different from the existing literature, our method enables us to deal with the problem without assuming regularity conditions on the controls, the convexity condition on the control domain, and some additional unnecessary conditions on the nonlinear terms of the integral equation and the cost functional.