A Fractional Differential Equation Model for Energy-Aware Trust-Based Security in Mobile-Agent Wireless Sensor Networks
Year: 2026
Type: preprint
Abstract: Wireless sensor networks must make routing and data-collection decisions under a persistent tension between security and energy expenditure. Trust scores can suppress compromised nodes, but frequent reputation updates and repeated authentication consume the same battery resources that the security layer is intended to protect. We formulate this interaction as a three-state Caputo fractional differential system coupling normalized residual energy, trust, and compromise probability. The fractional order 0 < α ≤ 1 provides a parsimonious memory parameter, while a bounded attack signal represents persistent selective forwarding and intermittent on–off behavior. A mobile-agent utility functional converts the state variables into an energy-aware forwarding decision. The model is shown to be well posed on finite horizons, and the physically meaningful cube [0, 1]3 is positively invariant under standard Caputo comparison assumptions. For constant attack intensity, the trust–compromise subsystem has a unique admissible equilibrium; its linearization satisfies the Matignon sector condition for every 0 < α ≤ 1. Hence the fractional order changes the transient memory profile without altering the constant-attack equilibrium. Numerical experiments based on a fractional Adams–Bashforth–Moulton predictor–corrector method quantify this distinction. Under burst attacks, decreasing α slows both trust degradation and compromise growth over the observation window and reduces energy depletion, but it also delays recovery and decision updates. The results therefore support a mechanism-level interpretation of fractional memory rather than the claim that fractionalization is intrinsically more secure. The framework provides a mathematically explicit basis for designing and testing energy-aware trust policies in mobile-agent wireless sensor networks. 2020 Mathematics Subject Classification: 26A33; 34A08; 34D20; 68M12.
Source: Research Square
Authors: Taylan Demi̇r, Shkelqim Hajrulla, Loubna Ali
Institutions: Ankara University, Epoka University
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213938153