Analytical stability analysis of the fractional-order particle swarm optimization algorithm

Mathematical modeling plays an important role in biology for describing the dynamics of infectious diseases. A useful strategy controlling infections and disorder conditions is to adopt computational algorithms determining interactions among their processes. The use fractional order (FO) calculus has been proposed as one relevant tool improving heuristic models. particles memory captured by FO derivative that opens door grasping long-term particle past behavior. This papers studies analytical convergence swarm optimization algorithm (FOPSO) based on a weak stagnation assumption. approach allows establishing systematic guidelines FOPSO parameters tuning. formulated basis control block diagram are represented nonlinear feedback. To describe historical evolution particles, state-space representation different types delayed discrete-time system. existence uniqueness equilibrium point discussed, stability analysis derived determine its boundaries. Several simulations confirm region point. also applied practical application, namely minimization blood glucose injection Type I diabetes mellitus patients.