Recursive-operational method for fractional systems

Author(s):  
Gabriel Bengochea ◽  
Manuel Ortigueira ◽  
Luis Verde-Star ◽  
António M. Lopes
2021 ◽  
Vol 10 (5) ◽  
pp. 325
Author(s):  
Ima Ituen ◽  
Baoxin Hu

Mapping and understanding the differences in land cover and land use over time is an essential component of decision-making in sectors such as resource management, urban planning, and forest fire management, as well as in tracking of the impacts of climate change. Existing methods sometimes pose a barrier to the effective monitoring of changes in land cover and land use, since a threshold parameter is often needed and determined based on trial and error. This study aimed to develop an automatic and operational method for change detection on a large scale from Moderate Resolution Imaging Spectroradiometer (MODIS) data. Super pixels were the basic unit of analysis instead of traditional individual pixels. T2 tests based on the feature vectors of temporal Normalized Difference Vegetation Index (NDVI) and land surface temperature were used for change detection. The developed method was applied to data over a predominantly vegetated area in northern Ontario, Canada spanning 120,000 sq. km from 2001–2016. The accuracies ranged between 78% and 88% for the NDVI-based test, from 74% to 86% for the LST-based test, and from 70% to 86% for the joint method compared with manual interpretation. Our proposed method for detecting land cover change provides a functional and viable alternative to existing methods of land cover change detection as it is reliable, repeatable, and free from uncertainty in establishing a threshold for change.


Author(s):  
Rachida Mezhoud ◽  
Khaled Saoudi ◽  
Abderrahmane Zaraï ◽  
Salem Abdelmalek

AbstractFractional calculus has been shown to improve the dynamics of differential system models and provide a better understanding of their dynamics. This paper considers the time–fractional version of the Degn–Harrison reaction–diffusion model. Sufficient conditions are established for the local and global asymptotic stability of the model by means of invariant rectangles, the fundamental stability theory of fractional systems, the linearization method, and the direct Lyapunov method. Numerical simulation results are used to illustrate the theoretical results.


2020 ◽  
Vol 23 (3) ◽  
pp. 723-752 ◽  
Author(s):  
Alessio Fiscella ◽  
Patrizia Pucci

AbstractThis paper deals with the existence of nontrivial solutions for critical possibly degenerate Kirchhoff fractional (p, q) systems. For clarity, the results are first presented in the scalar case, and then extended into the vectorial framework. The main features and novelty of the paper are the (p, q) growth of the fractional operator, the double lack of compactness as well as the fact that the systems can be degenerate. As far as we know the results are new even in the scalar case and when the Kirchhoff model considered is non–degenerate.


Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1464
Author(s):  
Vasily E. Tarasov

General fractional dynamics (GFDynamics) can be viewed as an interdisciplinary science, in which the nonlocal properties of linear and nonlinear dynamical systems are studied by using general fractional calculus, equations with general fractional integrals (GFI) and derivatives (GFD), or general nonlocal mappings with discrete time. GFDynamics implies research and obtaining results concerning the general form of nonlocality, which can be described by general-form operator kernels and not by its particular implementations and representations. In this paper, the concept of “general nonlocal mappings” is proposed; these are the exact solutions of equations with GFI and GFD at discrete points. In these mappings, the nonlocality is determined by the operator kernels that belong to the Sonin and Luchko sets of kernel pairs. These types of kernels are used in general fractional integrals and derivatives for the initial equations. Using general fractional calculus, we considered fractional systems with general nonlocality in time, which are described by equations with general fractional operators and periodic kicks. Equations with GFI and GFD of arbitrary order were also used to derive general nonlocal mappings. The exact solutions for these general fractional differential and integral equations with kicks were obtained. These exact solutions with discrete timepoints were used to derive general nonlocal mappings without approximations. Some examples of nonlocality in time are described.


2021 ◽  
Vol 31 (6) ◽  
pp. 063132
Author(s):  
Minjuan Yuan ◽  
Liang Wang ◽  
Yiyu Jiao ◽  
Wei Xu

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