Caputo–Fabrizio derivative provides stability solutions with non–immediate impulses of fractional differential

This study examines the HU-stability of a class of fractional functional differential systems including the “Caputo–Fabrizio derivative”, which is especially efficient in modelling systems with non-immediate impulses due of its non-singular, exponentially decaying kernel. Here the system is described across a piecewise interval with both differential and integral requirements, where the generalized fractional derivative is applied on subintervals and non-local integral restrictions are placed elsewhere. Functionals satisfying Lipschitz continuity control nonlinearities in the system, hence guaranteeing limitedness and regularity. The contraction criterion ρ < 1 is satisfied by the system over all admissible values of the fractional order δ ∈ (0,1) by use of analytical estimates and numerical validation. Tables and graphs show the changes of stability-related constants concerning δ, hence stressing the stabilizing function of the Caputo–Fabrizio derivative. The results verify that any approximate solution z(x) stays near the precise solution φ(x), hence confirming the HU-stability of the system and stressing its strength under perturbations.