Lagrange Adjoint System for Linear Fractional Systems with Distributed Delays
Abstract
In the present work we introduce an appropriate definition of the notion of a Lagrange (formal) adjoint system for homogeneous systems with incommensurate-order derivatives in Caputo’s sense and distributed delays. Under natural conditions, the existence and uniqueness of the adjoint fundamental matrix for these systems are proven, and an explicit relation between the resolvent of the formal adjoint system and the adjoint fundamental matrix is established. A generalization of the well-known Halanay relation is also introduced and proven. Furthermore, an explicit relation between the fundamental matrix and its adjoint fundamental matrix is established.
Fields of Study & Subjects
Nonlinear Differential Equations Analysis
Fractional Differential Equations Solutions
Stability and Control of Uncertain Systems
Publication details
- Journal / source
- Fractal and Fractional
- Publisher
- MDPI AG
- Volume
- 10
- Issue
- 3
- Pages
- 164–164
- Publication date
- 2 March 2026
- Language
- EN