A Fractional Cyber–Biological Model for Energy-Aware Trust-Based Mobile-Agent Wireless Sensor Networks: Secure Plant-Disease Surveillance

Low-power wireless sensor networks increasingly act as the measurement layer of biological decision systems, so a communication-security failure can propagate beyond the network and distort downstream biological inference. We formulate this interaction in two coupled layers. The cyber layer is a three-state Caputo fractional differential system for normalized residual energy, trust, and compromise probability under bounded selective-forwarding or on–off attack evidence. A mobile-agent utility rule converts these states into an energy-aware routing decision. The model is well posed on finite horizons, the physical cube [0, 1]3 is positively invariant, and the constant-attack trust–compromise equilibrium satisfies the Matignon sector condition for every 0 < α ≤ 1. Thus the fractional order changes transient memory without moving the constant-attack equilibrium. The biological layer is a plant-disease biosurveillance module: relative humidity, leaf wetness, and thermal suitability are combined into a normalized microclimate infection-suitability index, while cyber reliability states generate time-dependent fusion weights for competing sensor nodes. The fused signal drives a bounded disease-pressure equation used as a disease-generic biological decision state. A synthetic five-node greenhouse experiment couples an internal selective-forwarding episode to falsified microclimate data. For α = 0.85, trust-aware fusion reduces the attack-window root-mean-square error of the environmental suitability estimate from 0.07162 to 0.02818. The corresponding error in the downstream disease-pressure state decreases from 0.02059 to 0.00645. The improvement is not instantaneous: at attack onset, the previously trusted compromised node can transiently receive excessive weight before its trust state reacts. This delay exposes a genuine security– biology trade-off rather than an artificial claim that fractionalization is intrinsically beneficial. The resulting framework connects packet evidence, fractional cyber memory, secure sensor fusion, and biological risk estimation in a single reproducible model. 2020 Mathematics Subject Classification: 26A33; 34A08; 34D20; 68M12; 92C47; 92C80; 92D30.