A Refined Delta Laplace Transform Framework for Stability Assessment in Fractional‐Order Dynamical Systems

ABSTRACT This paper focuses on the stability analysis of delta fractional‐order systems with time delays. Several remarkable properties of the delta Laplace transform are exposed and discussed in detail, based on which the stability of delay delta fractional‐order systems is investigated systematically. Compared with existing results, this work achieves several key improvements: (i) the fractional‐order greater than one is considered for the first time; (ii) the delta Laplace transform is explored and adopted to simplify the stability analysis process; (iii) the area of the stable region is calculated quantitatively and analyzed with visualization methods. Numerical simulations are provided to demonstrate the validity and applicability of the theoretical findings, which also verify that the delta Laplace transform is an essential mathematical tool for analyzing delta fractional‐order systems.