FDA Express Vol. 35, No. 3, Jun 30, 2020
All issues: http://jsstam.org.cn/fda/
Editors: http://jsstam.org.cn/fda/Editors.htm
Institute of Soft Matter Mechanics, Hohai
University
For contribution:
shuhong@hhu.edu.cn,
fdaexpress@hhu.edu.com
For subscription:
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PDF download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol35_No3_2020.pdf
◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Fractional Calculus and the Future of Science (Special Issue in Entropy)
◆ Books
New Digital Signal Processing Methods: Applications to Measurement and Diagnostics
◆ Journals
Nonlinear Analysis-Hybrid Systems
◆ Paper Highlight
A fractional-order model for the novel coronavirus (COVID-19) outbreak
Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited
◆ Websites of Interest
Fractal Derivative and Operators and Their Applications
Fractional Calculus & Applied Analysis
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Latest SCI Journal Papers on FDA
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Euler-Maruyama scheme for Caputo stochastic fractional differential equations
By: Doan, T. S.; Huong, P. T.; Kloeden, P. E.; etc..
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 380 Published: DEC 15 2020
Shifted Jacobi spectral-Galerkin method for solving fractional order initial value problems
Can fractional calculus help improve tumor growth models?
Neumann method for solving conformable fractional Volterra integral equations
Legendre-collocation spectral solver for variable-order fractional functional differential equations
Approximate nonclassical symmetries for the time-fractional KdV equations with the small parameter
Impulsive initial value problems for a class of implicit fractional differential equations
A Study on Functional Fractional Integro-Differential Equations of Hammerstein type
By: Saeedi, Leila; Tari, Abolfazl; Babolian, Esmail
The solving integro-differential equations of fractional order with the ultraspherical functions
Solving fractional pantograph delay equations by an effective computational method
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Call for Papers
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Fractional Calculus and the Future of Science
(Special Issue in Entropy)
Three centuries ago, Newton transformed Natural Philosophy into today’s Science by focusing on change and quantification, and he did so in a way that resonated with the scientific community of his day. His arguments appeared to be geometric in character, and nowhere in the Principia do you find explicit reference to fluxions or to differentials. What Newton did was reveal the entailments of the calculus and convince generations of scientists of the value of their focusing on how physical objects change in space and time. Some contemporary mathematicians of his generation recognized what he had done, but their number could be counted on one hand, and their comments are primarily of historical interest only.
Fast-forward to today and Modern Science, from Anatomy to Zoology, is seen to have absorbed the transformational effect of Newton’s contribution to how we quantitatively and qualitatively understand the world, the fundamental importance of motion. However, it has occurred to a number of the more philosophically attuned contemporary scientists that we are now at another point of transition, where the implications of complexity, memory, and uncertainty have revealed themselves to be barriers to our future understanding of our technological society.
Topics (not limited to):
We are looking for imaginative articles that implement FC and reveal its transformational nature, including but not limited to such things as: how a fractional derivative in time incorporates memory into the solution of the dynamic description of an earthquake, a brain quake or a crash in the stock market; how the fractional derivative in space incorporates spatial nonlocality into the solution of the complex dynamical descriptions of a riot, the collective intelligence of social groups, or the neuronal activity of the brain; or how the combined fractional derivatives in both time and space of measures of uncertainty incorporate both memory and nonlocality into the phase space solution to capture the limited uncertainty of an ensemble of fractal trajectories, or the scaling behavior of complex dynamical networks.Manuscript Submission Information:
Deadline for manuscript submissions: 15 December 2020.
All details on this special section are now available at: https://www.mdpi.com/journal/entropy/special_issues/fract_future#info.
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Books
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New Digital Signal Processing Methods: Applications to Measurement and Diagnostics
(Authors: Raoul R. NigmatullinPaolo LinoGuido Maione)
Details:https://doi.org/10.1007/978-3-030-45359-6
Introduction
This book is intended as a manual on modern advanced statistical methods for signal processing. The objectives of signal processing are the analysis, synthesis, and modification of signals measured from different natural phenomena, including engineering applications as well. Often the measured signals are affected by noise, distortion and incompleteness, and this makes it difficult to extract significant signal information. The main topic of the book is the extraction of significant information from measured data, with the aim of reducing the data size while keeping the basic information/knowledge about the peculiarities and properties of the analyzed system; to this aim, advanced and recently developed methods in signal analysis and treatment are introduced and described in depth. More in details, the book covers the following new advanced topics (and the corresponding algorithms), including detailed descriptions and discussions: the Eigen-Coordinates (ECs) method, The statistics of the fractional moments, The quantitative "universal" label (QUL) and the universal distribution function for the relative fluctuations (UDFRF), the generalized Prony spectrum, the Non-orthogonal Amplitude Frequency Analysis of the Smoothed Signals (NAFASS), the discrete geometrical invariants (DGI) serving as the common platform for quantitative comparison of different random functions. Although advanced topics are discussed in signal analysis, each subject is introduced gradually, with the use of only the necessary mathematics, and avoiding unnecessary abstractions. Each chapter presents testing and verification examples on real data for each proposed method. In comparison with other books, here it is adopted a more practical approach with numerous real case studies.
Keywords:
Signal analysis; Data fitting; Optimal linear smoothing; Eigen-Coordinates; Reduced fractal models; Nonparametric methods; Statistics of fractional moments; Quantitative universal label; Fractal object; Generalized Prony spectrum; Self-similar properties; Quasi-periodic measurement; Quasi-reproducible experiments
Contents:
-Chapter 1: The Eigen-Coordinates Method: Reduction of Non-linear Fitting Problems
-Chapter 2: The Eigen-Coordinates Method: Description of Blow-Like Signals
-Chapter 3: The Statistics of Fractional Moments and its Application for Quantitative Reading of Real Data
-Chapter 4: The Quantitative “Universal” Label and the Universal Distribution Function for Relative Fluctuations. Qualitative Description of Trendless Random Functions
-Chapter 5: Description of Partly Correlated Random Sequences: Replacement of Random Sequences by the Generalised Prony Spectrum
-Chapter 6: The General Theory of Reproducible and Quasi-Reproducible Experiments
-Chapter 7: The Non-orthogonal Amplitude Frequency Analysis of Smoothed Signals Approach and Its Application for Describing Multi-Frequency Signals
-Chapter 8: Applications of NIMRAD in Electrochemistry
-Chapter 9: Reduction of Trendless Sequences of Data by Universal Parameters
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Journals
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Nonlinear Analysis-Hybrid Systems
(Selected)
Xiaohong Wang, Huaiqin Wu, Jinde Cao
Lyapunov and external stability of Caputo fractional order switching systems
Cong Wu, Xinzhi Liu
Dynamic cobweb models with conformable fractional derivatives
Martin Bohner, Veysel Fuat Hatipoğlu
Ruirui Duan, Junmin Li, Jiaxi Chen
Yushun Tan, Menghui Xiong, Dongsheng Du, Shumin Fei
Solutions of systems with the Caputo–Fabrizio fractional delta derivative on time scales
Dorota Mozyrska, Delfim F. M. Torres, Małgorzata Wyrwas
Zhi Li, Litan Yan
Guobao Liu, Ju H. Park, Shengyuan Xu, Guangming Zhuang
Stability, control and observation on non-uniform time domain
Mohamed Djemai, Michael Defoort, Anatoly A. Martynyuk
A novel approach to generate attractors with a high number of scrolls
J. L. Echenausía-Monroy, G. Huerta-Cuellar
Almost always observable hybrid systems
Claudio Arbib, Elena De Santis
Leader-following consensus for networks with single- and double-integrator dynamics
Ewa Girejko, Agnieszka B. Malinowska
Tobias Holicki, Carsten W. Scherer
Existence results for impulsive feedback control systems
Biao Zeng, Zhenhai Liu
New results on stability of random coupled systems on networks with Markovian switching
Pengfei Wang, Mengxin Wang, Huan Su
(Selected)
Clarify the physical process for fractional dynamical systems
Ping Zhou, Jun Ma, Jun Tang
Mohammed F. Tolba, Hani Saleh, Baker Mohammad, Mahmoud Al-Qutayri, Ahmed S. Elwakil, Ahmed G. Radwan
Analytical and numerical solution of an n-term fractional nonlinear dynamic oscillator
Ajith Kuriakose Mani, M. D. Narayanan
Fractional nonlinear dynamics of learning with memory
Vasily E. Tarasov
An experimental synthesis methodology of fractional-order chaotic attractors
C. Sánchez-López
Short memory fractional differential equations for new memristor and neural network design
Guo-Cheng Wu, Maokang Luo, Lan-Lan Huang, Santo Banerjee
Jianqiao Guo, Yajun Yin, Xiaolin Hu, Gexue Ren
RenMing Wang, YunNing Zhang, YangQuan Chen, Xi Chen, Lei Xi
Mittag–Leffler stability of nabla discrete fractional-order dynamic systems
Yingdong Wei, Yiheng Wei, Yuquan Chen, Yong Wang
The fractional derivative expansion method in nonlinear dynamic analysis of structures
Marina V. Shitikova
Clocking convergence of the fractional difference logistic map
Daiva Petkevičiūtė-Gerlach, Inga Timofejeva, Minvydas Ragulskis
Kui Ding, Quanxin Zhu
Zhang Zhe, Toshimitsu Ushio, Zhaoyang Ai, Zhang Jing
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Paper
Highlight
A fractional-order model for the novel coronavirus (COVID-19) outbreak
Karthikeyan Rajagopal, Navid Hasanzadeh, Fatemeh Parastesh, Ibrahim Ismael Hamarash, Sajad Jafari, Iqtadar Hussain
Publication information: Nonlinear Dynamics, Published 24 June 2020
https://doi.org/10.1007/s11071-020-05757-6
Abstract
The outbreak of the novel coronavirus (COVID-19), which was firstly reported in China, has affected many countries worldwide. To understand and predict the transmission dynamics of this disease, mathematical models can be very effective. It has been shown that the fractional order is related to the memory effects, which seems to be more effective for modeling the epidemic diseases. Motivated by this, in this paper, we propose fractional-order susceptible individuals, asymptomatic infected, symptomatic infected, recovered, and deceased (SEIRD) model for the spread of COVID-19. We consider both classical and fractional-order models and estimate the parameters by using the real data of Italy, reported by the World Health Organization. The results show that the fractional-order model has less root-mean-square error than the classical one. Finally, the prediction ability of both of the integer- and fractional-order models is evaluated by using a test data set. The results show that the fractional model provides a closer forecast to the real data.
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Fractional Langevin Equation Involving Two Fractional Orders: Existence and Uniqueness Revisited
Hossein Fazli, HongGuang Sun, Juan J. Nieto
Publication information: Mathematics, Volume 8, Issue5, Published 2020
https://doi.org/10.3390/math8050743
Abstract
We consider the nonlinear fractional Langevin equation involving two fractional orders with initial conditions. Using some basic properties of Prabhakar integral operator, we find an equivalent Volterra integral equation with two parameter Mittag–Leffler function in the kernel to the mentioned equation. We used the contraction mapping theorem and Weissinger’s fixed point theorem to obtain existence and uniqueness of global solution in the spaces of Lebesgue integrable functions. The new representation formula of the general solution helps us to find the fixed point problem associated with the fractional Langevin equation which its contractivity constant is independent of the friction coefficient. Two examples are discussed to illustrate the feasibility of the main theorems.
Keywords:
fractional Langevin equation; Mittag–Leffler function; Prabhakar integral operator; existence; uniqueness
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The End of This Issue
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