FDA Express Vol. 47, No. 1,
FDA Express Vol. 47, No. 1, Apr. 30, 2023
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.cn, fda@hhu.edu.cn
For subscription: http://jsstam.org.cn/fda/subscription.htm
PDF download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol 47_No 1_2023.pdf
◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
7th Conference on Numerical Methods for Fractional-derivative Problems
◆ Books
Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales
◆ Journals
Fractional Calculus and Applied Analysis
◆ Paper Highlight
Co-transport of arsenic and micro/nano-plastics in saturated soil
◆ 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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By: Dong, JB; Wu, Y; etc.
GEOMECHANICS AND GEOPHYSICS FOR GEO-ENERGY AND GEO-RESOURCES Volume: 9 Published: Dec 2023
By:Li, XY; Wen, CY; etc.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Volume: 38 Page:7246-7256 Published: Jul 2023
By:Xie, JQ; Yan, X; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 426 Published: Jul 2023
First attempt of barrier functions for Caputo's fractional-order nonlinear dynamical systems
By:Zhu, ZR; Huang, PF; etc.
SCIENCE CHINA-INFORMATION SCIENCES Volume: 66 Published: Jul 2023
By:Kalemkerian, J
JOURNAL OF STATISTICAL PLANNING AND INFERENCE Volume: 225 Page: 29-51 Published: Jul 2023
By:Li, J; Li, HL; etc.
COMPUTATIONAL & APPLIED MATHEMATICS Volume: 42 Published: Jun 2023
By:Shahid, S; Saifullah, S; etc.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume:22 Published:Jun 2023
By:Hernandez, E; Gambera, LR and dos Santos, JPC
APPLIED MATHEMATICS AND OPTIMIZATION Volume:87 Published: Jun 2023
Continuum limit of 2D fractional nonlinear Schrodinger equation
By: Choi, B and Aceves, A
JOURNAL OF EVOLUTION EQUATIONS Volume: 23 Published: Jun 2023
Extremal Positive Solutions for Hadamard Fractional Differential Systems on an Infinite Interval
By:Deren, FY and Cerdik, TS
MEDITERRANEAN JOURNAL OF MATHEMATICS Volume: 20 Published: Jun 2023
By:Kong, FC; Lu, DC; etc.
UNDERGROUND SPACE Volume: 10 Page:233-247 Published: Jun 2023
On Implicit k-Generalized ?-Hilfer Fractional Differential Coupled Systems with Periodic Conditions
By: Salim, A; Benchohra, M and Lazreg, JE
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: 22 Published: Jun 2023
Box Dimension and Fractional Integrals of Multivariate alpha-Fractal Functions
By:Agrawal, V; Pandey, M and Som, T
MEDITERRANEAN JOURNAL OF MATHEMATICS Volume:20 Published: Jun 2023
By:Das, A; Jain, R and Nashine, HK
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS Volume: 14 Published: Jun 2023
By: Zhang, J; Song, JB and Chen, HZ
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS Volume:15 Page:568-582 Published: Jun 2023
Results on the Approximate Controllability of Hilfer Type fractional Semilinear Control Systems
By:Vijayakumar, V; Malik, M and Shukla, A
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume:22 Published: Jun 2023
Normal extensions for degenerate conformable fractional a-order differential operator
By:Sertbas, M
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS Volume: 14 Published:Jun 2023 |
By:Alkhazzan, A; Wang, JG; etc.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: 22 Published: Jun 2023
By:Gan, D and Zhang, GF
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 423 Published: May 15 2023
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Call for Papers
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7th Conference on Numerical Methods for Fractional-derivative Problems
( July 27-29, 2023 in Beijing, China )
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:
- Fractional differential equations
- Fractional integral equations
- Numerical solutions
Organizers:
Martin Stynes, CSRC
Yongtao Zhou, Qingdao University of Technology, Qingdao
Guest Editors
Important Dates:
Deadline for conference receipts: June 14, 2023
All details on this conference are now available at: http://www.csrc.ac.cn/en/event/workshop/2023-03-17/115.html.
Mathematical Modeling of Anomalous Diffusion Phenomena Using Fractional Calculus: Theory and Applications
( A special issue of Fractal and Fractional )
Dear Colleagues: Fractional calculus is used in many scientific and technological fields, and its applications still finding new applicable areas. Fractional order derivatives have become an extremely important tool in mathematical modelling. Many phenomena in nature and physics can be modeled more efficiently by using fractional calculus; one of these is the phenomena of anomalous diffusion. Differential equations with fractional-order derivatives have found applications in the following problems: heat transfer in gels and porous materials; anomalous diffusion of drug release from a slab matrix; modeling of supercapacitor; modeling the phenomena of bacterial movement, or anomalous transport.
For this reason, the development of theories, methods of solving equations with fractional derivatives (analytical and numerical), and discovering further applications of fractional calculus is extremely important and interesting in science today. Therefore, we encourage scientists dealing with the topic of fractional calculus to consider submitting their research for publication in this Special Issue.
Keywords:
- Applications of fractional calculus
- Mathematical modeling using fractional derivatives
- Numerical and analytical methods for solving fractional differential equations
- Direct and inverse problems in modeling using fractional calculus
- Development of the theory related to fractional calculus
Organizers:
Prof. Dr. Damian Słota
Dr. Rafal Brociek
Dr. Agata Wajda
Guest Editors
Important Dates:
Deadline for manuscript submissions: 15 May 2023.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/9WHUM15LR8.
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Books
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Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales
( Authors: Svetlin G. Georgiev )
Details:https://doi.org/10.1007/978-3-319-73954-0
Book Description:
Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations.
Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales.
Author Biography:
Svetlin G. Georgiev, Faculty of Mathematics and Informatics, Sofia University St Kliment Ohridski, Sofia, Bulgaria
Contents:
Front Matter
Elements of Time Scale Calculus
Abstract; Forward and Backward Jump Operators, Graininess Function; Differentiation; Mean Value Theorems; Integration; The Exponential Function; Hyperbolic and Trigonometric Functions; Dynamic Equations; Power Series on Time Scales; Advanced Practical Problems; References;
The Laplace Transform on Time Scales
Abstract; Definition and Properties; The Laplace Transform on Isolated Time Scales; Advanced Practical Problems;
Convolution on Time Scales
Abstract; Shifts and Convolutions; Convolutions; The Convolution Theorem; Advanced Practical Problems;
The Riemann–Liouville Fractional Δ-Integral and the Riemann–Liouville Fractional Δ-Derivative on Time Scales
Abstract; The Δ-Power Function; Definition of the Riemann–Liouville Fractional Δ-Integral and the Riemann–Liouville Fractional Δ-Derivative; Properties of the Riemann–Liouville Fractional Δ-Integral and the Riemann–Liouville Fractional Δ-Derivative on Time Scales; Advanced Practical Problems;
Cauchy-Type Problems with the Riemann–Liouville Fractional Δ-Derivative
Abstract; Existence and Uniqueness of Solutions; The Dependence of the Solution on the Initial Data;
Riemann–Liouville Fractional Dynamic Equations with Constant Coefficients
Abstract; Homogeneous Riemann–Liouville Fractional Dynamic Equations with Constant Coefficients; Inhomogeneous Riemann–Liouville Fractional Dynamic Equations with Constant Coefficients; Advanced Practical Problems;
The Caputo Fractional Δ-Derivative on Time Scales
Abstract; Definition of the Caputo Fractional Δ-Derivative and Examples; Properties of the Caputo Fractional Δ-Derivative; Advanced Practical Problems;
Cauchy-Type Problems with the Caputo Fractional Δ-Derivative
Abstract; Existence and Uniqueness of the Solution to the Cauchy-Type Problem; The Dependence of the Solution on the Initial Value;
Caputo Fractional Dynamic Equations with Constant Coefficients
Abstract; Homogeneous Caputo Fractional Dynamic Equations with Constant Coefficients; Inhomogeneous Caputo Fractional Dynamic Equations with Constant Coefficients; Advanced Practical Problems;
Appendix: The Gamma Function
Abstract; Definition of the Gamma Function; Some Properties of the Gamma Function; Limit Representation of the Gamma Function;
Appendix: The Beta Function
Abstract; Definition of the Beta Function; Properties of the Beta Function; An Application;
Back Matter
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Journals
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(Selected)
Da-Sheng Mou, Chao-Qing Dai, Yue-Yue Wang
M. H. Heydari, M. Razzaghi
Feng-Xian Wang, Jie Zhang, Yan-Jun Shu, Xin-Ge Liu
Babak Shiri, Dumitru Baleanu
Modeling and analysis of Buck-Boost converter with non-singular fractional derivatives
Xiaozhong Liao, Yong Wang, etc.
Homan Emadifar, Kamsing Nonlaopon, etc.
Controlling fractional difference equations using feedback
Divya D. Joshi, Sachin Bhalekar, Prashant M. Gade
Muhammad Farman, Rabia Sarwar, Ali Akgul
Lifeng Lin, Tianzhen Lin, etc.
R. Kiruthika, R. Krishnasamy
Comparison principles for systems of Caputo fractional order ordinary differential equations
Cong Wu
Generalization of Mei symmetry approach to fractional Birkhoffian mechanics
Yi Zhang, Yun-Die Jia
Devendra Kumar, Ved Prakash Dubey, etc.
Asymptotic synchronization of second-fractional -order fuzzy neural networks with impulsive effects
Qiu Peng, Jigui Jian, etc.
Rami Ahmad El-Nabulsi, Waranont Anukool
Fractional Calculus and Applied Analysis
( Volume 26, issue 2 )
Lorenzo Cristofaro, Roberto Garra, Enrico Scalas & Ilaria Spassiani
Subordination and memory dependent kinetics in diffusion and relaxation phenomena
Katarzyna Górska & Andrzej Horzela
The fractional stochastic heat equation driven by time-space white noise
Rahma Yasmina Moulay Hachemi & Bernt Øksendal
Initial-boundary value problems for coupled systems of time-fractional diffusion equations
Zhiyuan Li, Xinchi Huang & Yikan Liu
Differentiation of integral Mittag-Leffler and integral Wright functions with respect to parameters
Alexander Apelblat & Juan Luis González-Santander
General one-dimensional model of the time-fractional diffusion-wave equation in various geometries
Ján Terpák
A Meyer-Itô formula for stable processes via fractional calculus
Alejandro Santoyo Cano & Gerónimo Uribe Bravo
Fudong Ge & YangQuan Chen
Infinitely many sign-changing solutions for a kind of fractional Klein-Gordon-Maxwell system
Li Wang, Liqin Tang & Jijiang Sun
Final value problem for Rayleigh-Stokes type equations involving weak-valued nonlinearities
Pham Thanh Tuan, Tran Dinh Ke & Nguyen Nhu Thang
Qiang Li & Xu Wu
Time-fractional integro-differential equations in power growth function spaces
Phung Dinh Tran, Duc Thanh Dinh, Tuan Kim Vu, M. Garayev & H. Guediri
Shouguo Zhu, Peipei Dai, Yinchun Qu & Gang Li
Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces
Pablo Ochoa
Monotonicity and uniqueness of positive solutions to elliptic fractional p-equations
Pengyan Wang
Towards to solution of the fractional Takagi–Taupin equations. The Green function method
Murat O. Mamchuev & Felix N. Chukhovskii
Symmetry of solutions for asymptotically symmetric nonlocal parabolic equations
Linfeng Luo & Zhengce Zhang
The existence and averaging principle for Caputo fractional stochastic delay differential systems
Mengmeng Li & Jinrong Wang
Dual Spaces of Anisotropic Variable Hardy–Lorentz Spaces and Their Applications
Jun Liu, Yaqian Lu & Long Huang
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Paper Highlight
Co-transport of arsenic and micro/nano-plastics in saturated soil Xiaoxiao Hao, HongGuang Sun, Yong Zhang, Shiyin Li, Zhongbo Yu
Publication information: Environmental Research Volume 228, 1 July 2023, 115871.
https://doi.org/10.1016/j.envres.2023.115871
Abstract
Contaminants can co-exist and migrate together in the environment, causing complex (and sometimes unexpected) transport dynamics which challenge the efficient remediation of individual contaminants. The co-transport dynamics, however, remained obscure for some contaminants, such as arsenic and micro/nano-plastics (MNPs). To fill this knowledge gap, this study explored the co-transport dynamics of arsenic and MNP particles in saturated soil by combining laboratory experiments and stochastic model analysis. Isothermal adsorption and sand column transport experiments showed that the adsorption of arsenic by MNP particles followed the Freundlich model, with a maximum adsorption of 2.425 mg/g for the MNP particles with a diameter of 100 nm. In the presence of MNP particles, the efflux concentration of arsenic ions declined due to adsorption, where the decline rate decreased with the increasing MNP size and increased with the increasing adsorption capacity. Experimental results also showed that the 100 nm nano-plastic particles prohibited arsenic transport in saturated sand columns, while the 5 μm microplastics enhanced arsenic transport due to electrostatic adsorption and media pore plugging. A tempered time fractional advective-dispersion equation was then proposed to quantify the observed breakthrough curves of arsenic. The results showed that this model can reliably capture the co-transport behavior of arsenic with MNPs in the saturated soil with all coefficients of determination over 0.97, and particularly, the small MNP particles facilitated anomalous transport of arsenic. This study therefore improved the understanding and quantification of the co-transport of arsenic and MNPs in soil..
Key Points
Arsenic; Polystyrene plastics; Co-transport; Fractional advective dispersion model
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Swapnil Mahadev Dhobale, Shyamal Chatterjee
A general class of optimal nonlinear resonant controllers of fractional order with time-delay for active vibration control – theory and experiment
Publication information: Mechanical Systems and Signal Processing Volume 182, 1 January 2023, 109580.
https://doi.org/10.1016/j.ymssp.2022.109580
Abstract
The present article generalizes the classical integer-order resonant controllers for active vibration control. The proposed controller utilizes a second-order linear filter with response feedback and a control input in the form of a nonlinear, time-delayed function of the fractional derivative of the filter variable. Thereby, the proposed controller encompasses the integer-order resonant controllers, like positive position feedback, acceleration feedback, negative velocity feedback, etc. as special cases and allows an extra degree of freedom in terms of choosing the optimum form of the control input function. Theoretical analysis of the system is performed by the method of multiple time scales and finally, the results are verified by numerical simulations and experiments. Two new numerical methods of parameters optimization are discussed. Detailed parametric studies are performed to reveal the effects of different design parameters, viz. the control gain, time-delay, and the fractional-order of the input function on the system performance. The theoretical and experimental studies demonstrate the supremacy of the fractional-order control over integer-order resonant control, especially for higher control gain and delay. The existence of an optimal value of the fractional order of the control function is established.
Keywords
Active vibration control; Resonant controller; Fractional derivative; Pole crossover design; Equal peak design
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