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This study presents methods of hygiene and the use of masks to control the disease. The zero basic reproduction number can be achieved by taking the necessary precautionary measures that prevent the transmission of infection, especially from uninfected virus carriers. The existence of time delay in implementing the quarantine strategy and the threshold values of the time delay that keeping the stability of the system are established. Also, it is found that keeping the infected people quarantined immediately is very important in combating and controlling the spread of the disease. Also, for special cases of the system parameters, the time delay can not affect the asymptotic behavior of the disease. Finally, numerical simulations have been illustrated to validate the theoretical analysis of the proposed model.

In this paper, the Adomian's decomposition method (ADM) is considered to solve a fractional advection-dispersion model. This model can be represented if the first order derivative in time is replaced by the Caputo fractional derivative of order α (0 < α ≤ 1). In addition, the space derivative orders are replaced by the alternative orders 0 < β ≤ 1 and 1 < γ ≤ 2. The obtained solutions are formulated in a convergent infinite series in terms of Mittage-Leffler functions. Finally, two illustrative examples are introduced to ensure the effectiveness of the used method.

In this article, two nonstandard high‐order schemes on a uniform and nonuniform time stepping combined with the multi‐parameter exponential fitting technique (MPEF) have been developed to solve the time‐fractional nonlinear reaction–diffusion system. The first method based on the MPEF combined with the 3‐weighted shifted‐Grünwald–Letnikov approximation with uniform time stepping, this scheme leads to a numerical solution that suffers from the singularity near t = 0. In order to frustrate this singularity, a nonstandard higher‐order L1‐approximation for a nonuniform time‐stepping scheme is developed. The developed scheme's convergence and unconditionally stability analysis have been verified. Numerical results effectively validate the theoretical aspects.

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In this paper, the variable order fractional permanent magnet synchronous motor (VOFPMSM) is investigated. Conditions for existence and uniqueness of the solution of the VOFPMSM are proposed. The stability behavior of the system's equilibrium points along with the variation of the motor parameters and the order of differentiation is discussed. Sufficient conditions that guarantee the asymptotic stability of each of the equilibrium points of the system are established. Also, the required conditions that give the effect of Hopf bifurcation of the system are established in terms of the system parameters and the order of differentiation and consequently the appearance of the chaotic behavior of the VOFPMSM. New numerical techniques based on the modified backward Euler's schemes for continuous and discontinuous variable order fractional model are presented. The obtained numerical results demonstrate the merits of the proposed method and the variable order fractional permanent magnet synchronous motor over the fractional permanent magnet synchronous motor.