Stability Criteria for Nonlinear-Truncated V-Fractional-Order Derivative Systems with Applications to Synchronization

This paper investigates the stability of nonlinear systems with truncated V-fractional-order derivatives. Initially, based on the fundamental properties of V-fractional calculus, the Bellman–Gronwall inequality for V-fractional α-differentiable functions is derived. Subsequently, several sufficient conditions for the stability of the considered systems are established via the Lyapunov direct method. For practical applications, multiple synchronization criteria for drive-response systems are further deduced by leveraging the aforementioned stability results. Finally, numerical examples are presented to verify the effectiveness and feasibility of the main theoretical findings.