scholarly journals Modeling third waves of Covid-19 spread with piecewise differential and integral operators: Turkey, Spain and Czechia

2021 ◽  
Author(s):  
Abdon Atangana ◽  
Seda IGRET ARAZ
Keyword(s):  
Infectious Disease ◽  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Numerical Solutions ◽  
Integral Operators ◽  
Stochastic Approach ◽  
Numerical Approach ◽  
Fractional Operators ◽  
Clear Indication

Several collected data representing the spread of some infectious disease have demonstrated that the spread does not really exhibit homogeneous spread. Clear examples can include the spread of Spanish ‡u and Covid-19. Collected data depicting numbers of daily new infections in the case of Covid-19 from countries like Turkey, Spain show three waves with different spread patterns. A clear indication of crossover behaviors. While modelers have suggested many mathematical models to depicting these behaviors, it becomes clear that their mathematical models cannot really capture the crossover behaviors, especially passage from deterministic resetting to stochastics. Very recently Atangana and Seda have suggested a concept of piecewise modeling consisting in defining a differential operator piece-wisely, the idea was first in chaos and outstanding patterns were captured. In this paper, we extend this concept to the field of epidemiology with the aim to depict waves with different patterns. Due to the novelty of this concept, a different approach to insure the existence and uniqueness of system solutions are presented. A piecewise numerical approach is presented to derive numerical solutions of such models. An illustrative example is presented and compared with collected data from 3 different countries including Turkey, Spain and Czechia. The obtained results let no doubt for us to conclude that this concept is a new window that will help mankind to better understand nature. Keywords: Piecewise modeling, piecewise existence and uniqueness, piecewise numerical scheme, Covid-19 model, fractional operators and stochastic approach.

scholarly journals A Quantum Model for the Dynamics of Cold Dark Matter

2019 ◽  
Vol 4 (4) ◽  
pp. 89
Author(s):  
Tim Zimmermann ◽  
Massimo Pietroni ◽  
Javier Madroñero ◽  
Luca Amendola ◽  
Sandro Wimberger
Keyword(s):  
Dark Matter ◽  
Numerical Scheme ◽  
Cold Dark Matter ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Equation System ◽  
Numerical Approach ◽  
Quantum Model ◽  
Numerical Examples ◽  
Key Features

A model for cold dark matter is given by the solution of a coupled Schrödinger–Poisson equation system. We present a numerical scheme for integrating these equations, discussing the problems arising from their nonlinear and nonlocal character. After introducing and testing our numerical approach, we illustrate key features of the system by numerical examples in 1 + 1 dimensions. In particular, we study the properties of asymptotic states to which the numerical solutions converge for artificial initial conditions.

scholarly journals ATANGANA–SEDA NUMERICAL SCHEME FOR LABYRINTH ATTRACTOR WITH NEW DIFFERENTIAL AND INTEGRAL OPERATORS

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040044
Author(s):  
ABDON ATANGANA ◽  
SEDA İĞRET ARAZ
Keyword(s):  
Numerical Simulations ◽  
Exponential Decay ◽  
Power Law ◽  
Real World ◽  
Numerical Scheme ◽  
Integral Operators ◽  
Fractional Operators ◽  
Mathematical Concepts ◽  
Newton Polynomial ◽  
Real World Problems

In this paper, we present a new numerical scheme for a model involving new mathematical concepts that are of great importance for interpreting and examining real world problems. Firstly, we handle a Labyrinth chaotic problem with fractional operators which include exponential decay, power-law and Mittag-Leffler kernel. Moreover, this problem is solved via Atangana-Seda numerical scheme which is based on Newton polynomial. The accuracy and efficiency of the method can be easily seen with numerical simulations.

PARALLEL SOLVER FOR THE SIMULATIONS OF DETONATION WAVES ON UNSTRUCTURED GRIDS

2020 ◽  
Author(s):  
A. I. Lopato ◽  
◽  
A. G. Eremenko ◽  
Keyword(s):  
Chemical Kinetics ◽  
Numerical Scheme ◽  
Unstructured Grids ◽  
Numerical Study ◽  
Numerical Approach ◽  
Detonation Waves ◽  
Detailed Chemical Kinetics ◽  
Parallel Solver ◽  
Further Development ◽  
Detailed Chemical

Recently, we developed a numerical approach for the simulation of detonation waves on fully unstructured grids and applied it to the numerical study of the mechanisms of detonation initiation in multifocusing systems. Current work is devoted to further development of our numerical approach, namely, parallelization of the numerical scheme and introduction of more comprehensive detailed chemical kinetics scheme.

scholarly journals Correctness conditions for high-order differential equations with unbounded coefficients

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kordan N. Ospanov
Keyword(s):  
Differential Equation ◽  
Hilbert Space ◽  
Existence And Uniqueness ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Order Linear Differential Equation ◽  
Unbounded Coefficients ◽  
Weighted Norms ◽  
Uniqueness Of The Solution ◽  
Linear Differential

AbstractWe give some sufficient conditions for the existence and uniqueness of the solution of a higher-order linear differential equation with unbounded coefficients in the Hilbert space. We obtain some estimates for the weighted norms of the solution and its derivatives. Using these estimates, we show the conditions for the compactness of some integral operators associated with the resolvent.

scholarly journals On integral inequalities related to the weighted and the extended Chebyshev functionals involving different fractional operators

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Barış Çelik ◽  
Mustafa Ç. Gürbüz ◽  
M. Emin Özdemir ◽  
Erhan Set
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Operators ◽  
Fractional Integral Operators

AbstractThe role of fractional integral operators can be found as one of the best ways to generalize classical inequalities. In this paper, we use different fractional integral operators to produce some inequalities for the weighted and the extended Chebyshev functionals. The results are more general than the available classical results in the literature.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

scholarly journals The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986654 ◽  
Author(s):  
Muhammad Altaf Khan
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Parameter ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Fractional Operators ◽  
Fundamental Properties ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Model Apply

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

scholarly journals Use of Jacobians for inverse kinematics of articulated robots : a study on approximate solutions

2020 ◽  
Author(s):  
◽  
Uriel Jacket Tresor Demby's
Keyword(s):  
Numerical Solution ◽  
Inverse Kinematics ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Fuzzy Inference ◽  
Numerical Approach ◽  
Data Driven ◽  
Approximate Methods ◽  
Inference System ◽  
First Case

In the context of articulated robotic manipulators, the Forward Kinematics (FK) is a highly non-linear function that maps joint configurations of the robot to poses of its endeffector. Furthermore, while in the most useful cases these functions are neither injective (one-to-one) nor surjective (onto), depending on the robot configuration -- i.e. the sequence of prismatic versus revolute joints, and the number of Degrees of Freedom (DoF) -- the associated Inverse Kinematics (IK) problem may be practically or even theoretically impossible to be solved analytically. Therefore, in the past decades, several approximate methods have been developed for many instances of IK problems. The approximate methods can be divided into two distinct categories: data-driven and numerical approaches. In the first case, data-driven approaches have been successfully used for small workspace domains (e.g., task-driven applications), but not fully explored for large ones, i.e. in task-independent applications where a more general IK is required. Similarly, and despite many successful implementations over the years, numerical solutions may fail if an improper matrix inverse is employed (e.g., Moore-Penrose generalized inverse). In this research, we propose a systematic, robust and accurate numerical solution for the IK problem using the Unit-Consistent (UC) and the Mixed (MX) Inverse methods to invert the Jacobians derived from the Denavit-Hartenberg (D-H) representation of the FK for any robot. As we demonstrate, this approach is robust to whether the system is underdetermined (less than 6 DoF) or overdetermined (more than 6 DoF). We compare the proposed numerical solution to data driven solutions using different robots -- with DoF varying from 3 to 7. We conclude that numerical solutions are easier to implement, faster, and more accurate than most data-driven approaches in the literature, specially for large workspaces as in task-independent applications. We particularly compared the proposed numerical approach against two data-driven approaches: Multi-Layer Perceptron (MLP) and Adaptive Neuro-Fuzzy Inference System (ANFIS), while exploring various architectures of these Neural Networks (NN): i.e. number of inputs, number of outputs, depth, and number of nodes in the hidden layers.

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