Some novel mathematical analysis on the fractional‐order 2019‐nCoV dynamical model

“…Using dynamical systems described by fractional differential equations (FDEs) has become a way to understand complex materials and processes [10]. FDEs are capable of modeling non-locality, memory, spatial heterogeneity, and anomalous diffusion that are inherent in many real-world problems, making them useful in fields such as dynamical modeling [11], biology [12], chemistry [13], hydrology [14], control, signal and image processing, and finance [15].…”

Section: Introductionmentioning

confidence: 99%

New Perturbation–Iteration Algorithm for Nonlinear Heat Transfer of Fractional Order

Abdel Aal

2024

Fractal Fract

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Ordinary differential equations have recently been extended to fractional equations that are transformed using fractional differential equations. These fractional equations are believed to have high accuracy and low computational cost compared to ordinary differential equations. For the first time, this paper focuses on extending the nonlinear heat equations to a fractional order in a Caputo order. A new perturbation iteration algorithm (PIA) of the fractional order is applied to solve the nonlinear heat equations. Solving numerical problems that involve fractional differential equations can be challenging due to their inherent complexity and high computational cost. To overcome these challenges, there is a need to develop numerical schemes such as the PIA method. This method can provide approximate solutions to problems that involve classical fractional derivatives. The results obtained from this algorithm are compared with those obtained from the perturbation iteration method (PIM), the variational iteration method (VIM), and the Bezier curve method (BCM). All solutions are tested with numerical simulations. The study found that the new PIA algorithm performs better than the PIM, VIM, and BCM, achieving high accuracy and low computational cost. One significant advantage of this algorithm is that the solutions obtained have established that the fractional values of alpha, specifically α, significantly influencing the accuracy of the outcome and the associated computational cost.

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“…In India, 90% of the population has received the first dose, and 70% have been given both doses of the vaccine [15] . However, the COVID-19 vaccines could not offer a 100% protection against the infection due to the discoveries of new variants [16] . This is evident from many cases of post-vaccination infections that have been reported.…”

Section: Introductionmentioning

confidence: 99%

“…The study of Owoyemi et al. [16] made a generalization of an integer-order mathematical model describing the transmission dynamics of COVID-19 to a fractional-order version in the sense of Caputo fractional derivative. In a similar study, El-Sayed et al.…”

Section: Introductionmentioning

confidence: 99%