Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data

Qureshi, Sania; Bonyah, Ebenezer

doi:10.1016/j.physa.2019.122496

Cited by 37 publications

(18 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some more applications of this concept can be found in diffusion, groundwater flow problem, and groundwater pollution problems 16–26 . Very recently, the application of this concept was extended to capture chaotic attractors and even to describe the spread of infectious diseases within a given population 27–37 . The results obtained from these studies were similar to those obtained from classical fractional differential and integral operators, a proof and validity of nonlocality of this calculus more precisely the associate integral display properties similar to those of the Riemann‐Liouville integral.…”

Section: Introductionmentioning

confidence: 56%

New chaotic attractors: Application of fractal‐fractional differentiation and integration

Gómez‐Aguilar

Atangana

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

Very recently, the concept of fractal differentiation and fractional differentiation has been combined to produce new differentiation operators. The new operators were constructed using three different kernels, namely, power law, exponential decay, and the generalized Mittag‐Leffler function. The new operators have two parameters: the first is considered as fractional order and the second as fractal dimension. In this work, we applied these new operators to model some chaotic attractors, and the models were solved numerically using a new and very efficient numerical scheme. We presented numerical simulations for some specific fractional order and fractal dimension. The classical fractional differential models could be recovered when the fractal dimension is equal to 1; in these cases, the obtained attractors with power law presented no similarities. Nevertheless, those obtained via Caputo‐Fabrizio and the Atangana‐Baleanu derivative show some crossover effects, which is due to non‐index law property. However, those obtained from fractal‐fractional, in particular, those with the Mittag‐Leffler kernel, show very strange and new attractors with self‐similarities; these results are obtained for the first time. We conclude that this new concept is the future to modelling complexities with self‐similarities.

show abstract

Section: Introductionmentioning

confidence: 56%

New chaotic attractors: Application of fractal‐fractional differentiation and integration

Gómez‐Aguilar

Atangana

2020

Math Methods in App Sciences

View full text Add to dashboard Cite

show abstract

“…This section investigates the numerical solution of the fractional model (9) and to present the simulation results for various values of model parameters and

. In order to do this, we utilize the Euler’s type approach presented discussed in the recent literature and references therein [32] , [33] . To obtain the iterative scheme, let us express the fractional model (9) in the following simple form:

where

is used for a continuous real valued vector function, which additionally satisfies the Lipschitz condition and

stands for initial state vector.…”

Section: Numerical Solution Of Fractional Modelmentioning

confidence: 99%

Modeling and simulation of the novel coronavirus in Caputo derivative

et al. 2020

View full text Add to dashboard Cite

The Coronavirus disease or COVID-19 is an infectious disease caused by a newly discovered coronavirus. The COVID-19 pandemic is an inciting panic for human health and economy as there is no vaccine or effective treatment so far. Different mathematical modeling approaches have been suggested to analyze the transmission patterns of this novel infection. this paper, we investigate the dynamics of COVID-19 using the classical Caputo fractional derivative. Initially, we formulate the mathematical model and then explore some the basic and necessary analysis including the stability results of the model for the case when . Despite the basic analysis, we consider the real cases of coronavirus in China from January 11, 2020 to April 9, 2020 and estimated the basic reproduction number as . The present findings show that the reported data is accurately fit the proposed model and consequently, we obtain more realistic and suitable parameters. Finally, the fractional model is solved numerically using aÂ numerical approach and depicts many graphical results for the fractional order of Caputo operator. Furthermore, some key parameters and their impact on the disease dynamics are shown graphically.

show abstract

“…The parameters obtained in (25) can also be used to determine new fractional masks in determining the edges of the images as follows:…”

Section: Mask Ta3mentioning

confidence: 99%

Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels

2020

View full text Add to dashboard Cite

Computers and electronics play an enormous role in today's society, impacting everything from communication and medicine to science. The development of computer-related technologies has led to the emergence of many new important interdisciplinary fields, including the field of image processing. Image processing tries to find new ways to access and extract information from digital images or videos. Due to this great importance, many researchers have tried to utilize new and powerful tools introduced in pure and applied mathematics to develop new concepts in imaging science. One of these valuable research areas is the contents of fractional differential calculus. In recent years, extensive applications to the new fractional operators have been employed in real-world problems. This article attempts to address a practical aspect of this era of research in the edge detecting of an image. For this purpose, two general structures are first proposed for making new fractional masks. Then the components in these two structures are evaluated using the fractional integral Atangana-Baleanu operator. The performance and effectiveness of these proposed designs are illustrated by several numerical simulations. A comparison of the results with the results of several well-known masks in the literature indicates that the results presented in this article are much more accurate and efficient. This is the main achievement of this article. These fractional masks are all novel and have been introduced for the first time in this contribution. Moreover, in terms of computational cost, the proposed fractional masks require almost the same amount of computations as the existing conventional ones. By observing the numerical simulations presented in the paper, it is easily understood that with proper adjustment for the fractional-order parameter, the accuracy of the obtained results can be significantly improved. Each of the new suggested structures in this article can be regarded as a valid and effective alternative for the well-known existing kernels in identifying the edges of an image.

show abstract

Classical and contemporary fractional operators for modeling diarrhea transmission dynamics under real statistical data

Cited by 37 publications

References 31 publications

New chaotic attractors: Application of fractal‐fractional differentiation and integration

New chaotic attractors: Application of fractal‐fractional differentiation and integration

Modeling and simulation of the novel coronavirus in Caputo derivative

Some new edge detecting techniques based on fractional derivatives with non-local and non-singular kernels

Contact Info

Product

Resources

About