In this paper, we analyzed and found the solution for a suitable nonlinear fractional dynamical system that describes coronavirus (2019-nCoV) using a novel computational method. A compartmental model with four compartments, namely, susceptible, infected, reported and unreported, was adopted and modified to a new model incorporating fractional operators. In particular, by using a modified predictor–corrector method, we captured the nature of the obtained solution for different arbitrary orders. We investigated the influence of the fractional operator to present and discuss some interesting properties of the novel coronavirus infection.

The Korteweg–De Vries (KdV) equation has always provided a venue to study and generalizes diverse physical phenomena. The pivotal aim of the study is to analyze the behaviors of forced KdV equation describing the free surface critical flow over a hole by finding the solution with the help of q-homotopy analysis transform technique (q-HATT). he projected method is elegant amalgamations of q-homotopy analysis scheme and Laplace transform. Three fractional operators are hired in the present study to show their essence in generalizing the models associated with power-law distribution, kernel singular, non-local and non-singular. The fixed-point theorem employed to present the existence and uniqueness for the hired arbitrary-order model and convergence for the solution is derived with Banach space. The projected scheme springs the series solution rapidly towards convergence and it can guarantee the convergence associated with the homotopy parameter. Moreover, for diverse fractional order the physical nature have been captured in plots. The achieved consequences illuminates, the hired solution procedure is reliable and highly methodical in investigating the behaviours of the nonlinear models of both integer and fractional order.

The Atangana–Baleanu derivative and the Laguerre polynomial are used in this analysis to define a new computational technique for solving fractional differential equations. To serve this purpose, we have derived the operational matrices of fractional integration and fractional integro-differentiation via Laguerre polynomials. Using the derived operational matrices and collocation points, we reduce the fractional differential equations to a system of linear or nonlinear algebraic equations. For the error of the operational matrix of the fractional integration, an error bound is derived. To illustrate the accuracy and the reliability of the projected algorithm, numerical simulation is presented, and the nature of attained results is captured in diverse order. Finally, the achieved consequences enlighten that the solutions obtained by the proposed scheme give better convergence to the actual solution than the results available in the literature.

In order to depict a situation of possible spread of infection from prey to predator, a fractional-order model is developed and its dynamics is surveyed in terms of boundedness, uniqueness, and existence of the solutions. We introduce several threshold parameters to analyze various points of equilibrium of the projected model, and in terms of these threshold parameters, we have derived some conditions for the stability of these equilibrium points. Global stability of axial, predator-extinct, and disease-free equilibrium points are investigated. Novelty of this model is that fractional derivative is incorporated in a system where susceptible predators get the infection from preys while predating as well as from infected predators and both infected preys and predators do not reproduce. The occurrences of transcritical bifurcation for the proposed model are investigated. By finding the basic reproduction number, we have investigated whether the disease will become prevalent in the environment. We have shown that the predation of more number of diseased preys allows us to eliminate the disease from the environment, otherwise the disease would have remained endemic within the prey population. We notice that the fractional-order derivative has a balancing impact and it assists in administering the co-existence among susceptible prey, infected prey, susceptible predator, and infected predator populations. Numerical computations are conducted to strengthen the theoretical findings.

Wireless sensor networks (WSNs) are subject to cyber attacks. Security of such networks is a significant priority for everyone. Due to the network's frail defense mechanisms, WSNs are easy targets for worm attacks. A single unsecured node via contact can effectively propagate the worm across the entire network. Mathematical epidemic models are helpful in analyzing worm propagation in WSNs. To understand the attacking and spreading dynamics of worms in WSNs, a fractional‐order compartmental epidemic model is investigated with susceptible, exposed, infected, recovered, and vaccinated nodes. Dynamical aspects such as boundedness, existence, and uniqueness of the solutions are presented with the help of fractional calculus theory. Global stability of the points of equilibrium are established. The projected nonlinear structure is examined numerically via the generalized Adams–Bashforth–Moulton method. This study demonstrates the influence of the fractional operator on WSNs dynamics and the efficiency of the numerical method.