Retraction Note: Fractional-order scheme for bovine babesiosis disease and tick populations

Efficient modeling schemes currently exist to handle the spatially variable-order fractional Laplacians in the fractional Laplacian viscoacoustic wave equation. The simplest approach is to change the spatially variable-order fractional Laplacians into a linear combination of several constant fractional-order Laplacians. We generalize the constant fractional-order scheme to a spatially variable fractional-order viscoelastic wave equation and develop an almost-equivalent constant fractional-order viscoelastic wave equation. Our constant fractional-order scheme avoids the simulation error introduced by directly averaging the spatially varying fractional order; thus, our scheme simulates seismic wave propagation in viscoelastic media with sharp [Formula: see text] contrasts well. The fast Fourier transform is used in the approximation of the fractional Laplacians, which improves the spectral accuracy in space. Several simulation examples are performed to verify that the numerical solution of a homogeneous [Formula: see text] model obtained by solving our constant fractional-order viscoelastic wave equation agrees well with that obtained by solving the original viscoelastic wave equation. The numerical simulations for spatially varying [Formula: see text] models obtained by the new wave equation are more straightforward than those currently in use and match the reference solutions obtained by accurate, but inefficient, methods. This match of simulation results verifies the accuracy of our viscoelastic wave equation.

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A Fractional-Order Epidemic Model for Bovine Babesiosis Disease and Tick Populations

Abstract and Applied Analysis ◽

10.1155/2015/729894 ◽

2015 ◽

Vol 2015 ◽

pp. 1-10 ◽

Cited By ~ 6

Author(s):

José Paulo Carvalho dos Santos ◽

Lislaine Cristina Cardoso ◽

Evandro Monteiro ◽

Nelson H. T. Lemes

Keyword(s):

Differential Equations ◽

Fractional Order ◽

Fractional Differential Equations ◽

Epidemic Model ◽

Equilibrium Points ◽

Biological Behavior ◽

Bovine Babesiosis ◽

Comparison Theory ◽

Linearization Theorem ◽

Fractional Differential

This paper shows that the epidemic model, previously proposed under ordinary differential equation theory, can be generalized to fractional order on a consistent framework of biological behavior. The domain set for the model in which all variables are restricted is established. Moreover, the existence and stability of equilibrium points are studied. We present the proof that endemic equilibrium point when reproduction numberR0>1is locally asymptotically stable. This result is achieved using the linearization theorem for fractional differential equations. The global asymptotic stability of disease-free point, whenR0<1, is also proven by comparison theory for fractional differential equations. The numeric simulations for different scenarios are carried out and data obtained are in good agreement with theoretical results, showing important insight about the use of the fractional coupled differential equations set to model babesiosis disease and tick populations.

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Retraction notice to: ‘Assembly of efficient Ag/n-Si/Cu2CdSnS4/Au 5 for photovoltaic cell utilities’

The European Physical Journal Applied Physics ◽

10.1051/epjap/210010s ◽

2020 ◽

Vol 93 (3) ◽

pp. 30302

Author(s):

Halemah I. El Saeedy ◽

Hanan A. Yakout ◽

Mona Mahmoud ◽

Said A. Abdelaal ◽

Mardia T. El Sayed

Keyword(s):

Electron Microscopy ◽

Photovoltaic Cell ◽

Careful Consideration ◽

Applied Physics ◽

Fundamental Nature ◽

Link Type ◽

Retraction Notice

Refers to RETRACTED: Assembly of efficient Ag/n-Si/Cu2CdSnS4/ Au for photovoltaic cell utilities, Halemah I. El Saeedy, Hanan A. Yakout, Mona Mahmoud, Said A. Abdelaal, and Mardia T. El Sayed, Eur. Phys. J. Appl. Phys. 92, 30302 (2020) https://doi.org/10.1051/epjap/2020200207. published online 17 December 2020 At the request of the Authors, the following article has been retracted. The following article has been retracted. Shortly after publication, the Editorial Board of EPJ Applied Physics received comments from a specialist in electron microscopy and analysis. He pointed out that the paper presented severe errors dealing with the microanalysis spectrum presented in one of the figures. As a conclusion, the presented EDS spectrum could not correspond to the studied sample. After careful consideration, the Editorial Board of EPJ Applied Physics asked for the retraction of this paper, due to the fundamental nature of the mistakes in the data and analysis of EDS spectrum, upon which the conclusion of the paper was incorrectly found. The Authors accept this decision and request the retraction of the paper.

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