A Fractional Framework for Modeling Malicious Code Spread in Wireless Sensor Networks

This paper develops a fractional six-compartment model to describe malware spread in wireless sensor networks. To represent actual network activity, the model is constructed using generalized proportional-Caputo operators that incorporate memory and tempering effects. The existence and uniqueness of solutions are proved by applying fixed-point theorems. The stability of the system is then studied using the Ulam–Hyers approach and its extended form. A fractional Adams predictor–corrector method is employed to illustrate the dynamics. The results suggest that memory and tempering play an important role in shaping infection patterns, and they indicate that fractional calculus can provide a useful framework for studying and managing malware in distributed sensor networks.