On solutions of some delay Volterra integral problems on a half-line

Abstract

In this paper, we study the existence of a.e. monotonic solutions of some general delay integral problems for both fractional and integer orders in the space of Lebesgue integrable functions on the interval R+ = [0;1) and in the space of locally integrable functions L1loc (R+). In particular, the uniqueness of solutions for considered problems is obtained.

Optimal Solutions for a Class of Impulsive Differential Problems with Feedback Controls and Volterra-Type Distributed Delay: A Topological Approach

“…In these cases, depending on the material used, the deflections of the beam (or arm) can significantly affect the system's current state, and thus, in these cases as well, the problem is better defined if a delay term is included in the equation. To explore these topics further, we refer to the papers [1,5,10,19,22,24] and books [15,25], acknowledging that they do not represent an exhaustive bibliography on the problem. In this article, by way of example, we will demonstrate the application of our results to a population dynamics model.…”

“…The set { f n } n∈N is integrably bounded. Indeed, by (F4) and (6), and recalling that y ∈ X (see(19)), for a.e. t ∈ [a, b] we get…”