Fractional Dynamics and Fractal Geometry for Robust Fault Detection in Wireless Sensor Networks

A novel event detection framework for wireless sensor networks (WSNs) is presented, integrating fractional-order calculus and fractal ‎geometry to address fault tolerance and detection accuracy challenges. The methodology comprises five synergistic components: mul-‎multifractal event region simulation, fractional-order dynamic trust evaluation, Monte Carlo-based event estimation guided by fractional ‎information gain, fractional-order fault propagation modelling, and a multi-layer fractional consensus mechanism. These components ‎enable the system to adaptively assess node reliability, predict fault propagation, and detect spatially complex events with high precision. ‎The framework's simulation results demonstrate significant outperformance over conventional methods (binary decision trees, majority ‎voting, and Shannon-entropy-based detection), achieving 96.2% detection accuracy, a 1.8% false positive rate, a 0.982 area under the ‎curve, and a 28.4% reduction in data transmission overhead. These improvements highlight the practical potential of integrating fractional-‎al and fractal intelligence in the design of robust, memory-aware, and energy-efficient WSNs architectures suitable for harsh and dynamic-‎ic environments deployment‎.