A CAPUTO-FABRIZIO FRACTIONAL MODEL OF NICHOLSON'S BLOWFLIES: EXISTENCE, UNIQUENESS, AND STABILITY ANALYSIS

Abstract

This paper introduces a novel formulation of the Nicholson's blowies modelusing the Caputo-Fabrizio fractional derivative, which features a non-singular exponentialkernel. This approach enhances the classical model by capturing memory effects and hereditarycharacteristics inherent in population dynamics while preserving analytical tractabilityand compatibility with standard initial conditions. Using fixed point theory, we establishsucient conditions for the existence, uniqueness, and Ulam-Hyers-type stability of solutionsto the proposed fractional-order system. Additionally, we extend the framework to more realisticbiological scenarios involving harvesting, impulsive effects, and stochastic inuences.The theoretical results are supported by numerical simulations that illustrate the dynamicalbehavior of the model and conrm its robustness under perturbations.