Malaysian Journal of Mathematical Sciences, March 2026, Vol. 20, No. 1
A Study on the Fractional-Order Linear Dynamical System with Time-Varying Delays and Fracture
Sehar, R. and Zehra, A.
Corresponding Email: rimshasehar1997@gmail.com
Received date: 5 December 2024
Accepted date: 13 August 2025
Abstract:
This article is about the study of a novel concept of finite-time stability of a fractional-order dynamical system with time-varying delays and fracture. We have obtained the solution and established stability conditions of the system. Moreover, the controllability and observability conditions in the form of Gramian matrices and matrix conditions are derived based upon the well-known Kalman rank criteria. The results obtained are novel, and to facilitate a better understanding, we have included several illustrative examples.
Keywords: Caputo fractional derivative; time-varying delay; fracture; finite-time stability; controllability and observability.
