FDA Express Vol. 43, No. 2, May 31, 2022

发布时间:2022-05-31 访问量:1739

FDA Express    Vol. 43, No. 2, May 31, 2022

 

All issues: http://jsstam.org.cn/fda/

Editors: http://jsstam.org.cn/fda/Editors.htm

Institute of Soft Matter Mechanics, Hohai University
For contribution: jyh17@hhu.edu.cnfda@hhu.edu.cn

For subscription: http://jsstam.org.cn/fda/subscription.htm

PDF download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol 43_No 2_2022.pdf


 

◆  Latest SCI Journal Papers on FDA

(Searched on May 31, 2022)

 

  Call for Papers

Fractional Calculus, Control Theory and Applications

6th Conference on Numerical Methods for Fractional-derivative Problems


 

◆  Books

Fractional Derivative Modeling in Mechanics and Engineering

 

◆  Journals

Applied Mathematics and Computation

Fractional Calculus and Applied Analysis

 

  Paper Highlight

Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics

Anomalous diffusion and asymmetric tempering memory in neutrophil chemotaxis

 

  Websites of Interest

Fractal Derivative and Operators and Their Applications

Fractional Calculus & Applied Analysis

 

 

 

 

 

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 Latest SCI Journal Papers on FDA

------------------------------------------

(Searched on May 31, 2022)



 Some evaluations of the fractional p-Laplace operator on radial functions

By: Colasuonno, F; Ferrari, F; etc.
MATHEMATICS IN ENGINEERING Volume: 5 Published: 2023


 Convoluted fractional differentials of various forms utilizing the generalized Raina's function description with applications

By: Ibrahim, RW and Baleanu, D
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 16 Page:432-441 Published: ‏ Dec 31 2022



 A metaheuristic approach for interval type-2 fuzzy fractional order fault-tolerant controller for a class of uncertain nonlinear system

By: Patel, HR and Shah, VA
AUTOMATIKA Volume:63  Page:656-675  Published: ‏ Dec 2 2022



 Novel chaos game optimization tuned-fractional-order PID fractional-order PI controller for load-frequency control of interconnected power systems

By:Barakat, M
PROTECTION AND CONTROL OF MODERN POWER SYSTEMS Volume: ‏7 Published: Dec 2022



 On generalized fractional integral with multivariate Mittag-Leffler function and its applications

By: Nazir, A; Rahman, G; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: ‏ 61 Page: 9187-9201 Published: Nov 2022



 A Robust Fractional-Order Control Technique for Stable Performance of Multilevel Converter-Based Grid-Tied DG Units

By: Zafari, A; Mehrasa, M; etc.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Volume: ‏69 Page: 10192-10201 Published: ‏ Oct 2022



 Ulam-Hyers-Rassias Mittag-Leffler stability for the darboux problem for partial fractional differential equations

By:Ben Makhlouf, A and Boucenna, D
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS Volume:51 Page:1541-1551 Published: Oct 2022



 A fractional order control model for Diabetes and COVID-19 co-dynamics with Mittag-Leffler function

By:Omame, A; Nwajeri, UKK; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: ‏ 61 Page:7619-7635 Published: ‏ Oct 2022



 Stochastic stability analysis of a fractional viscoelastic plate excited by Gaussian white noise

By: Hu, DL; Mao, XC and Han, L
MECHANICAL SYSTEMS AND SIGNAL PROCESSING Volume: 177 Published: ‏Sep 1 2022



 A Tikhonov regularization method for solving a backward time-space fractional diffusion problem

By:Feng, XL; Zhao, MX and Qian, Z
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: ‏411 Published: Sep 2022



 Recovery of advection coefficient and fractional order in a time-fractional reaction-advection-diffusion-wave equation

By:Zhang, Y; Wei, T and Yan, XB
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 411 Published: Sep 2022



 Numerical analysis of Atangana-Baleanu fractional model to understand the propagation of a novel corona virus pandemic

By: Butt, AIK; Ahmad, W; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: ‏ 61 Page: 7007-7027 Published: ‏ Sep 2022



 Fractional Moisil-Teodorescu operator in elasticity and electromagnetism

By:Bory-Reyes, J; Perez-de la Rosa, MA and Pena-Perez, Y
IEEE TRANSACTIONS ON POWER ELECTRONICS Volume: ‏ 61 Page:6811-6818 Published: ‏ Sep 2022



 Computational and numerical simulations of nonlinear fractional Ostrovsky equation

By:Omri, M; Abdel-Aty, AH; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page:6887-6895 Published: Sep 2022



 Fractional order model for complex Layla and Majnun love story with chaotic behaviour

By: Farman, M; Akgul, A; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: ‏ 61 Page:6725-6738 Published: ‏ Sep 2022



 Controllability analysis of multiple fractional order integro-differential damping systems with impulsive interpretation

By: Jothilakshmi, G; Vadivoo, BS; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: ‏410 Published: ‏ Aug 15 2022



 A weak Galerkin/finite difference method for time-fractional biharmonic problems in two dimensions

By:Yazdani, A; Momeni, H and Cheichan, MS
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 410 Published:Aug 15 2022 |



 A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations

By:Khan, H; Alam, K; etc.
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: ‏ 198 Page:455-473 Published: Aug 2022



 Application of modified extended tanh method in solving fractional order coupled wave equations

By: Dubey, S and Chakraverty, S
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 198 Page:509-520 Published: Aug 2022


 

 

 

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Call for Papers

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Fractional Calculus, Control Theory and Applications

( A special issue of Fractal and Fractional )


Dear Colleagues: Fractional models have become increasingly relevant for dealing with some phenomena in a wide array of scientific and technological fields.

This is the case because it has become clear that such models are more likely to capture effects such as anomalous phenomena, and more generally phenomena with memory effects, contrary to the traditional models of ordinary and partial differential equations. Although fractional calculus is almost as old as calculus itself, the realization of its usefulness for concrete models is rather recent. A few examples of its applications in this field include material science, rheology, and anomalous diffusion.

Along with the models under consideration, one naturally must consider the control-theoretic aspects thereto associated.

The present volume aims to collect original research papers and surveys with meaningful contributions to fractional calculus in relation to its applications to phenomena in the physical and biological sciences and beyond, as well as the controllability, observability, and stabilizability properties of fractional differential equations, and corresponding numerical aspects. It is intended to provide results which will also be accessible to those interested in implementing the models in concrete situations in the industrial and economic contexts.

Keywords:

- Fractional PDEs
- Controllability, observability and stabilizability
- Optimization, optimal control
- Applications to life science
- Nonlocal PDEs



Organizers:

Prof. Dr. Mahamadi Warma
Prof. Dr. Valentin Keyantuo
Prof. Dr. Carlos Lizama
Guest Editors

Important Dates:

Deadline for manuscript submissions: 30 June 2022.

All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/FCCTA.



6th Conference on Numerical Methods for Fractional-derivative Problems

( August 11-13, 2022 )


Dear Colleagues: In recent years there has been an explosion of research activity in numerical methods for fractional-derivative(FD) differential equations. Much of the published work has been concerned with solutions to FD problems that are globally smooth --- but simple examples show that for given smooth data, the solutions to FD problems typically have weak singularities at some boundary of the domain, so globally smooth solutions are very unusual.

This conference will focus on the numerical solution of more typical (and more difficult) FD problems whose solutions exhibit weak singularities. As the definitions of fractional derivatives are nonlocal, there is also the issue of how to avoid excessive memory storage and expensive calculations in their implementation. Thus there are two objectives to this research:

(i) the design and analysis of methods (finite difference, finite element, ...) for FD problems;
(ii) the efficient computation of numerical solutions.


Keywords:

- Finite difference
- Finite element
- The efficient computation of numerical solutions



Important Dates:

Deadline for manuscript submissions: for registration and abstract submission will be in July 2022--details for this will appear later.

All details on this conference are now available at: http://www.csrc.ac.cn/en/event/workshop/2022-05-25/113.html.





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Books

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Fractional Derivative Modeling in Mechanics and Engineering

( Authors: Wen Chen, HongGuang Sun, Xicheng Li )

Details:https://doi.org/10.1007/978-981-16-8802-7

Book Description:

This book highlights the theory of fractional calculus and its wide applications in mechanics and engineering. It describes research findings in using fractional calculus methods for modeling and numerical simulation of complex mechanical behavior. It covers the mathematical basis of fractional calculus, the relationship between fractal and fractional calculus, unconventional statistics and anomalous diffusion, typical applications of fractional calculus, and the numerical solution of the fractional differential equation. It also summaries the latest findings, such as variable order derivative, distributed order derivative, and its applications. The book avoids lengthy mathematical demonstrations and presents the theories related to the applications in an easily readable manner. This textbook intends for students, researchers, and professionals in applied physics, engineering mechanics, and applied mathematics. It is also of high reference value for those in environmental mechanics, geotechnical mechanics, biomechanics, and rheology.


Author Biography:

Dr. Wen Chen is a Distinguished Professor and former Dean of the College of Mechanics and Materials at Hohai University, China. His research covers computational mechanics, hydrodynamics, and acoustics. His research interests include RBF-based numerical simulation, anomalous diffusion, and non-local statistics of soft matter mechanics. He also serves as Associate Director of the Chinese Society of Environmental Mechanics and the TC member on Linear Control Systems of the International Federation of Automatic Control. He is former TC Chair of the sector in computational mechanics software, China Mechanics Society.

Dr. Hongguang Sun works as a Professor in the College of Mechanics and Materials, Director of Sino-US Joint Research Center of Groundwater and Environmental Fluid Mechanics, and Deputy Director of the Institute of Hydraulics and Fluid Mechanics, Hohai University, China. His main research interests include simulation and remediation of groundwater and soil pollution, sediment transport, and high-precision computational mechanics.

Dr. Xicheng Li works as an Associate Professor at the School of Mathematical Sciences, the University of Jinan, China. He has been engaged in theoretical and applied research of fractional calculus, especially fractional derivative modeling of anomalous diffusion. He is also done much exploration in modeling heat and mass transfer and solving fractional differential equations.

Contents:

Front Matter

Introduction
Abstract; History of Fractional Calculus; Geometric and Physical Interpretation of Fractional Derivative Equation; Application in Science and Engineering; Anomalous Diffusion Modeling in Environmental Mechanics; Constitutive Relation of Viscoelasticity; Biomedical Science; System Control; References;

Mathematical Foundation of Fractional Calculus
Abstract; Definition of Fractional Calculus; Properties of Fractional Calculus; Fourier and Laplace Transforms of the Fractional Calculus; Analytical Solution of Fractional-Order Equations; Questions and Discussions; Notes; References;

Fractal and Fractional Calculus
Abstract; Fractal Introduction and Application; The Relationship Between Fractional Calculus and Fractal; References;

Fractional Diffusion Model, Anomalous Statistics and Random Process
Abstract; The Fractional Derivative Anomalous Diffusion Equation; Statistical Model of the Acceleration Distribution of Turbulence Particle;Lévy Stable Distributions; Stretched Gaussian Distribution; Tsallis Distribution; Ito Formula; Random Walk Model; Discussion; References;

Typical Applications of Fractional Differential Equations
Abstract; Power-Law Phenomena and Non-Gradient Constitutive Relation; Fractional Langevin Equation; The Complex Damped Vibration; Viscoelastic and Rheological Models; The Power-Law Frequency Dependent Acoustic Dissipation; The Fractional Variational Principle of Mechanics; Fractional Schrödinger Equation; Other Application Fields; Variable-Order, Distributed-Order and Random-Order Fractional Derivative Models with Its Applications; Some Applications of Fractional Calculus in Biomechanics; Some Applications of Fractional Calculus in the Modeling of Drug Release Process; References;

Numerical Methods for Fractional Differential Equations
Abstract; Time-Fractional Differential Equations (TFDEs); Space Fractional Differential Equations (SFDEs); Open Issues of Numerical Methods for FDEs; Numerical Methods for Fractal Derivative Equations; Numerical Methods for Positive Fractional Derivative Equations; References;

Current Development and Perspectives of Fractional Calculus
Abstract; Summary and Discussion; Perspectives;

Back Matter



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 Journals

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Applied Mathematics and Computation

 (Selected)

 


 Leibniz-type rule of variable-order fractional derivative and application to build Lie symmetry framework

Zhi-Yong Zhang, Cheng-Bao Liu


 Acceleration of the order of convergence of a family of fractional fixed-point methods and its implementation in the solution of a nonlinear algebraic system related to hybrid solar receivers

A. Torres-Hernandez, F. Brambila-Paz, R. Montufar-Chaveznava


 Bipartite leader-following synchronization of fractional-order delayed multilayer signed networks by adaptive and impulsive controllers

Ying Guo, Yuze Li


 Fast method and convergence analysis for the magnetohydrodynamic flow and heat transfer of fractional Maxwell fluid

Yi Liu, Xiaoqing Chi, Xiaoyun Jiang


 Event-triggered impulsive synchronization of fractional-order coupled neural networks

Hailian Tan, Jianwei Wu, Haibo Bao


 A fast algorithm for two-dimensional distributed-order time-space fractional diffusion equations

Lu-Yao Sun, Zhi-Wei Fang, etc.


 A novel and efficient operational matrix for solving nonlinear stochastic differential equations driven by multi-fractional Gaussian noise

Tahereh Eftekhari, Jalil Rashidinia


 Adaptive quasi-synchronization control of heterogeneous fractional-order coupled neural networks with reaction-diffusion

Wei Chen, Yongguang Yu, etc.


 Numerical analysis for compact difference scheme of fractional viscoelastic beam vibration models

Qing Li, Huanzhen Chen, etc.


 The application of the distributed-order time fractional Bloch model to magnetic resonance imaging

Qiang Yu, Ian Turner


 Relative controllability analysis of fractional order differential equations with multiple time delays

B. S. Vadivoo, G. Jothilakshmi


 A fractional variational image denoising model with two-component regularization terms

Xiao Li, Xiaoying Meng, Bo Xiong.


 Pointwise error estimate and stability analysis of fourth-order compact difference scheme for time-fractional Burgers’ equation

Qifeng Zhang, Cuicui Sun, etc.


 Arbitrarily high-order trapezoidal rules for functions with fractional singularities in two dimensions

Senbao Jiang, Xiaofan Li.


 H∞ output feedback control for fractional-order T-S fuzzy model with time-delay

Jinghua Ning, Changchun Hua

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Fractional Calculus and Applied Analysis

  (Volume 25, issue 1)

 


  On the fractional Laplacian of variable order

Eric Darve, Marta D’Elia, Roberto Garrappa, Andrea Giusti, Natalia L. Rubio


 Fractional boundary value problems

Mirko D’Ovidio


 Integral operators defined “up to a polynomial”

Serena Dipierro, Aleksandr Dzhugan, Enrico Valdinoci


 An inverse problem of determining orders of systems of fractional pseudo-differential equations

Ravshan Ashurov, Sabir Umarov


 CTRW modeling of quantum measurement and fractional equations of quantum stochastic filtering and control

Vassili Kolokoltsov


 Upper and lower estimates for the separation of solutions to fractional differential equations

Kai Diethelm, Hoang The Tuan


 Asymptotic cycles in fractional maps of arbitrary positive orders

Mark Edelman, Avigayil B. Helman


 Convolution series and the generalized convolution Taylor formula

Yuri Luchko


 Bounds for mixing times for finite semi-Markov processes with heavy-tail jump distribution

Nicos Georgiou, Enrico Scalas


 Stochastic solutions for time-fractional heat equations with complex spatial variables

Luisa Beghin, Alessandro De Gregorio


 Sequential generalized Riemann–Liouville derivatives based on distributional convolution

Tillmann Kleiner, Rudolf Hilfer


 A higher order resolvent-positive finite difference approximation for fractional derivatives on bounded domains

Boris Baeumer, Mihály Kovács, Matthew Parry

 

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 Paper Highlight

Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics

Yingjie Liang, Yue Yu, Richard L. Magin  

Publication information: Fractional Calculus and Applied Analysis: Published: 25 April 2022

https://doi.org/10.1007/s13540-022-00020-8


Abstract

The inverse Mittag–Leffler function has been used to model the logarithmic growth of the mean squared displacement in anomalous diffusion, the restricted mobility of membrane proteins, and the slow viscoelastic creep observed in glasses. These applications are hindered because the inverse Mittag–Leffler function has no explicit form and cannot be approximated by existing methods in the domain x∈(0,+∞). This study proposes a conversion method to compute the inverse Mittag–Leffler function in terms of the Mittag–Leffler function. The new method uses the one- and two-parameter Mittag–Leffler function to compute the inverse Mittag–Leffler function in the target domain. We apply this method to fit data collected in studies of: (i) the ultraslow mobility of beta-barrel proteins in bacterial membranes, (ii) the ultraslow creep observed in high strength self-compacting concrete, and (iii) the ultraslow relaxation seen in various glasses. The results show that the inverse Mittag–Leffler function can capture ultraslow dynamics in all three cases. This method may also be extended to other generalized logarithmic laws.


Keywords

Inverse Mittag–Leffler function (primary ); Mittag–Leffler function; Ultraslow diffusion; Ultraslow relaxation; Ultraslow creep

 

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Anomalous diffusion and asymmetric tempering memory in neutrophil chemotaxis

  Peter DieterichID1, Otto Lindemann, etc.

Publication information: PLoS Computational Biology: Published: May 18, 2022
https://doi.org/10.1371/journal.pcbi.1010089


 

Abstract

The motility of neutrophils and their ability to sense and to react to chemoattractants in their environment are of central importance for the innate immunity. Neutrophils are guided towards sites of inflammation following the activation of G-protein coupled chemoattractant receptors such as CXCR2 whose signaling strongly depends on the activity of Ca2+ permeable TRPC6 channels. It is the aim of this study to analyze data sets obtained in vitro (murine neutrophils) and in vivo (zebrafish neutrophils) with a stochastic mathematical model to gain deeper insight into the underlying mechanisms. The model is based on the analysis of trajectories of individual neutrophils. Bayesian data analysis, including the covariances of positions for fractional Brownian motion as well as for exponentially and power-law tempered model variants, allows the estimation of parameters and model selection. Our model-based analysis reveals that wildtype neutrophils show pure superdiffusive fractional Brownian motion. This so-called anomalous dynamics is characterized by temporal long-range correlations for the movement into the direction of the chemotactic CXCL1 gradient. Pure superdiffusion is absent vertically to this gradient. This points to an asymmetric ‘memory’ of the migratory machinery, which is found both in vitro and in vivo. CXCR2 blockade and TRPC6-knockout cause tempering of temporal correlations in the chemotactic gradient. This can be interpreted as a progressive loss of memory, which leads to a marked reduction of chemotaxis and search efficiency of neutrophils. In summary, our findings indicate that spatially differential regulation of anomalous dynamics appears to play a central role in guiding efficient chemotactic behavior..


Author summary:

Neutrophil granulocytes are essential for the first host defense. After leaving the blood circulation they migrate efficiently towards sites of inflammation. They are guided by chemoattractants released from cells within the inflammatory foci. On a cellular level, directional migration is a consequence of cellular front-rear asymmetry which is induced by the concentration gradient of the chemoattractants. The generation and maintenance of this asymmetry, however, is not yet fully understood. Here we analyzed the paths of chemotacting neutrophils with different stochastic models to gain further insight into the underlying mechanisms. Wildtype chemotacting neutrophils show an anomalous superdiffusive behavior. CXCR2 blockade and TRPC6-knockout cause the tempering of temporal correlations and a reduction of chemotaxis. Importantly, such tempering is found both in vitro and in vivo. These findings indicate that the maintenance of anomalous dynamics is crucial for chemotactic behavior and the search efficiency of neutrophils.

 

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The End of This Issue

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