Stability analysis for a class of triangular systems with general conformable derivative

ABSTRACT Fractional calculus, particularly the conformable fractional derivative, has gained significant attention for its ability to extend classical differentiation to noninteger orders while preserving essential properties and incorporating memory effects into system models. This paper focuses on the stability analysis of triangular systems characterized by generalized conformable derivatives, leveraging their partitioned structure to simplify analysis. By constructing a Lyapunov‐like function tailored to the generalized conformable derivative framework, we derive sufficient conditions for practical uniform stability and asymptotic convergence of system states, even in the presence of nonlinear perturbations and parameter variations. Unlike previous works that rely on the Caputo derivative, our approach employs the generalized conformable derivative, overcoming its limitations and extending the analysis to a broader class of nonlinear systems. This generalization enhances both theoretical robustness and practical applicability, offering more flexible stability criteria for complex systems. The paper concludes with illustrative examples and future research directions, highlighting the framework's potential to advance fractional‐order stability analysis.