The impact of Caputo-Fabrizio fractional derivative and the dynamics of noise on worm propagation in wireless IoT networks

Abstract

The main objective of this article on Wireless sensor network of the Internet of Things (IoT). The wireless network, B bluetooth network, infrared network, and other networks are the key components of the Internet of Things (IoT). The major emphasis of this work was on the impact of Caputo-Fabrizio fractional derivative on worm propagation in heterogeneous susceptible-exposed-infected-recovered wireless IoT devices. We first determined the equilibrium points and fundamental reproduction number for the Caputo-Fabrizio HSEIR system, and then we discussed the stability of the system at the worm propagation equilibrium point. Using the Picard-Lindeof method, we determine the existence and unique solution for the fractional CF system of the heterogeneous SEIR model. Next, we use fixed point theory to judge the stability of the iterative method. We investigate the impact of the derivative order on the behaviour of the resultant functions and acquired numerical values by computing the model's findings for various fractional orders. In addition, we compute the integer-order model's results and contrast them with the results of the fractional-order model. We develop a periodically intermittent controller driven by white noise with the amazing benefits of reduced cost and more adaptable control technique to restrict the spread of worms in wireless IoT networks. To clearly define the conditions for stability in probability one, we employ the stochastic analysis technique. Our results show that the nonlinear worm propagation system may be stabilised by intermittent stochastic perturbation under the parameters of intermittent time linked to stochastic perturbation strength. Our theoretical conclusions may be used to analyse the observable processes of the worm, design countermeasures to prevent its spread, and evaluate the consequences of various system parameters.