FDA Express Vol. 50, No. 3
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 50_No 3_2024.pdf
◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
8th Conference on Numerical Methods for Fractional-derivative Problems
Fractional- and Integer-Order System: Control Theory and Applications, 2nd Edition
◆ Books
◆ Journals
Fractional Calculus and Applied Analysis
◆ Paper Highlight
A Unified Phenomenological Model Captures Water Equilibrium and Kinetic Processes in 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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Existence and stability of solution for time-delayed nonlinear fractional differential equations
By: Kebede, SG and Lakoud, AG
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Volume: 32 Published: Dec 31 2024
By:Hasan, AKM; Sarkar, DK; etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 18 Published: Dec 31 2024
By:Alqahtani, AM and Prasad, JG
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Volume: 32 Published: Dec 31 2024
By:Alabedalhadi, M; Al-Omari, S; etc.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Page:102510 Volume: 32 Published: Dec 31 2024
By:Ma, YL; Maryam, M; etc.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: 23 Published: Jul 2024
An efficient spectral method for the fractional Schrödinger equation on the real line
By:Shen, MX and Wang, HY
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume:444 Published:Jul 2024
By:Khan, HNA; Zada, A and Khan, I
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume:23 Published:Jul 2024
By:Kumar, GR; Ramesh, K; etc.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume:23 Published: Jul 2024
On a System of Sequential Caputo-Type p-Laplacian Fractional BVPs with Stability Analysis
By: Waheed, H; Zada, A; etc
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: 23 Published: Jul 2024
By:Matar, MM; Samei, ME; etc.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: 23 Published: Jul 2024
By:Zhou, HC; Qian, JY and Cai, RY
APPLIED MATHEMATICS AND COMPUTATION Volume: 470 Published: Jun 2024
Investigation of controllability and stability of fractional dynamical systems with delay in control
By: Selvam, AP and Govindaraj, V
MATHEMATICS AND COMPUTERS IN SIMULATION Volume:220 Page:89-104 Published: Jun 2024
By:Cai, YY and Sun, HW
APPLIED MATHEMATICS AND COMPUTATION Volume: 470 Published: Jun 2024
Existence of solutions to a system of fractional three-point boundary value problem at resonance
By:Sun, RP and Bai, ZB
APPLIED MATHEMATICS AND COMPUTATION Volume: 470 Published: Jun 2024
By:Zhuang, Q; Heryudono, A;
APPLIED MATHEMATICS AND COMPUTATION Volume:469 Published: May 15 2024
By:Wei, C; Wang, XP; etc.
NEURAL NETWORKS Volume:173 Published: May 2024
By:Meng, YX and He, XM
ACTA MATHEMATICA SCIENTIA Volume: 44 Page:997-1019 Published:May 2024
By:Wang, Y; Qiu, YJ and Yin, QP
ACTA MATHEMATICA SCIENTIA Volume: 44 Page:1020-1035 Published: May 2024
Reconfigurable Fractional-Order Operator and Bandwidth Expansion Suitable for PIα Controller
By:Prommee, P and Pienpichayapong, P
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Volume: 71 Page:5126-5136 Published: May 2024
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Call for Papers
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8th Conference on Numerical Methods for Fractional-derivative Problems
( July 8-11, 2024 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:
- Numerical Methods
- Fractional-derivative Problems
- Finite difference, finite element
Organizers:
Martin Stynes, CSRC
Guest Editors
Important Dates:
Deadline for conference receipts: June 25, 2024.
All details on this conference are now available at: https://www.csrc.ac.cn/en/event/workshop/2024-02-19/119.html.
Fractional- and Integer-Order System: Control Theory and Applications, 2nd Edition
( A special issue of Fractal and Fractional )
Dear Colleagues: Over the last two decades, (fractional) differential equations have become more common in physics, signal processing, fluid mechanics, viscoelasticity, mathematical biology, electrochemistry, and many other fields, allowing for a new and more realistic way to capture memory-dependent phenomena and irregularities within systems through more sophisticated mathematical analysis. As a result of its growing applications, the study of the stability of (fractional) differential equations has received significant attention. Furthermore, in recent years, interest in fractional- and integer-order controllers has grown. Examples of these are optimal control, CRONE controllers, fractional PID controllers, lead–lag compensators, and sliding mode control.
The purpose of this Special Issue is to disseminate research on fractional-/integer-order control theory and its applications in practical systems modeled using fractional-/integer-order differential equations. These include the design, implementation, and application of fractional-/integer-order control to electrical circuits and systems, mechanical systems, chemical systems, biological systems, finance systems, and so on.
Keywords:
- Control theory for fractional- and integer-order systems;
- Lyapunov-based stability and stabilization of fractional- and integer-order systems;
- Feedback linearization-based controller and observer design for fractional- and integer-order systems;
- Digital implementation of fractional- and integer-order control;
- Sliding mode control of fractional- and integer-order systems;
- Finite-, fixed-, and predefined-time stability and stabilization of fractional- and integer-order systems;
- Set-membership design for fractional- and integer-order systems;
- High-gain based observers and differentiator design for fractional- and integer-order systems;
- Event-based control of fractional- and integer-order systems;
- Incremental stability of fractional- and integer-order systems;
- Control of non-minimum phase systems using fractional- and integer-order theory;
- New physical interpretation of fractional- and integer-order operators and their relationship to control design;
- Design and development of efficient battery management and state of health estimation using fractional- and integer-order calculus;
- Applications of fractional- and integer-order control to electrical, mechanical, chemical, financial, and biological systems;
- Verification and reachability analysis of fractional- and integer-order differential equations.
Organizers:
Dr. Thach Ngoc Dinh
Dr. Shyam Kamal
Dr. Rajesh Kumar Pandey
Prof. Dr. Bijnan Bandyopadhyay
Prof. Dr. Jun Huang
Guest Editors
Important Dates:
Deadline for manuscript submissions: 10 April 2024.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/6YHE43DGYS.
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Books
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Fractional-order Modeling of Nuclear Reactor: From Subdiffusive Neutron Transport to Control-oriented Models
( Authors: Vishwesh Vyawahare , Paluri S. V. Nataraj )
Details:https://doi.org/10.1007/978-981-10-7587-2
Book Description:
This book addresses the topic of fractional-order modeling of nuclear reactors. Approaching neutron transport in the reactor core as anomalous diffusion, specifically subdiffusion, it starts with the development of fractional-order neutron telegraph equations. Using a systematic approach, the book then examines the development and analysis of various fractional-order models representing nuclear reactor dynamics, ultimately leading to the fractional-order linear and nonlinear control-oriented models. The book utilizes the mathematical tool of fractional calculus, the calculus of derivatives and integrals with arbitrary non-integer orders (real or complex), which has recently been found to provide a more compact and realistic representation to the dynamics of diverse physical systems. Including extensive simulation results and discussing important issues related to the fractional-order modeling of nuclear reactors, the book offers a valuable resource for students and researchers working in the areas of fractional-order modeling and control and nuclear reactor modeling.
Author Biography:
Vishwesh Vyawahare, Ramrao Adik Institute of Technology, Navi Mumbai, India
Paluri S. V. Nataraj, Indian Institute of Technology Bombay, Mumbai, India
Contents:
Front Matter
Fractional Calculus
Abstract; Introduction; Special Functions in Fractional Calculus; Fractional-order Integrals and Derivatives: Definitions; Fractional-order Differential Equations; Fractional-order Systems; Chapter Summary;
Introduction to Nuclear Reactor Modeling
Abstract; Introduction; Nuclear Reactor Theory; Slab Reactor; Mathematical Modeling of Nuclear Reactor; Anomalous Diffusion; Fractional Calculus Applications in Nuclear Reactor Theory; Chapter Summary;
Development and Analysis of Fractional-order Neutron Telegraph Equation
Abstract; Introduction; Motivation; Derivation of FO Neutron Telegraph Equation Model; Analysis of Mean-Squared Displacement; Solution Using Separation of Variables Method; Chapter Summary;
Development and Analysis of Fractional-order Point Reactor Kinetics Model
Abstract; Introduction; Point Reactor Kinetics Model; Derivation of FPRK Model; Solution of FPRK Model with One Effective Delayed Group; Chapter Summary;
Further Developments Using Fractional-order Point Reactor Kinetics Model
Abstract; Introduction; Fractional Inhour Equation; Inverse FPRK Model; Constant Delayed Neutron Production Rate Approximation; Prompt Jump Approximation; Zero Power Transfer Function of the Reactor; Chapter Summary;
Development and Analysis of Fractional-order Point Reactor Kinetics Models with Reactivity Feedback
Abstract; Modeling of Reactivity Feedback in a Reactor; Fractional-order Nordheim–Fuchs Model; FPRK Model with Reactivity Feedback (Below Prompt Critical); Linearized FO Model with Reactivity Feedback; Chapter Summary;
Development and Analysis of Fractional-order Two-Group Models and Fractional-order Nodal Model
Abstract; IO Two-Group Diffusion Model; Fractional-order Two-Group Telegraph-Subdiffusion Model; Fractional-order Two-Group Subdiffusion Model; Fractional-order Nodal Model; Chapter Summary;
Back Matter
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Journals
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(Selected)
X.Y. Li, B.Y. Wu, X.Y. Liu
Solving a fractional chemotaxis system with logistic source using a meshless methods
Antonio M. Vargas
A new method of solving the Riesz fractional advection–dispersion equation with nonsmooth solution
Hong Du, Zhong Chen
Stability of conformable fractional delay differential systems with impulses
Danhua He, Liguang Xu
Asymptotically linear magnetic fractional problems
Rossella Bartolo, Pietro d’Avenia, Giovanni Molica Bisci
Zhiyong Xing, Haiqing Zhang, Nan Liu
Sharp analysis of L1−2 method on graded mesh for time fractional parabolic differential equation
Jiliang Cao, Wansheng Wang, Aiguo Xiao
Variable-step numerical schemes and energy dissipation laws for time fractional Cahn–Hilliard model
Ren-jun Qi, Wei Zhang, Xuan Zhao
Long-time behavior for the Kirchhoff diffusion problem with magnetic fractional Laplace operator
Jiabin Zuo, Juliana Honda Lopes, Vicenţiu D. Rădulescu
Romeo Martínez, Armando Gallegos, Jorge E. Macías-Díaz
Pavel Řehák
Shi-Ping Tang, Yu-Mei Huang
The existence theory of solution in Sobolev space for fractional differential equationsn
Ying Sheng, Tie Zhang
Jungang Wang, Qingyang Si, Jia Chen, You Zhang
Sen Wang, Xian-Feng Zhou, Denghao Pang, Wei Jiang
Fractional Calculus and Applied Analysis
( Volume 27, Issue 2 )
Ziqiang Li, Yubin Yan
Analysis of a class of completely non-local elliptic diffusion operators
Yulong Li, Emine Çelik, Aleksey S. Telyakovskiy
Orlicz-Lorentz-Karamata Hardy martingale spaces: inequalities and fractional integral operators
Zhiwei Hao, Libo Li, Long Long & Ferenc Weisz
Representations of solutions of systems of time-fractional pseudo-differential equations
Sabir Umarov
Time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative
Ravshan Ashurov & Rajapboy Saparbayev
Schrödinger-Maxwell equations driven by mixed local-nonlocal operators
Nicolò Cangiotti, Maicol Caponi, Alberto Maione & Enzo Vitillaro
Analysis of BURA and BURA-based approximations of fractional powers of sparse SPD matrices
Nikola Kosturski & Svetozar Margenov
Nabil Chems Eddine, Maria Alessandra Ragusa & Dušan D. Repovš
Discrete convolution operators and equations
Rui A. C. Ferreira & César D. A. Rocha
Rachid Echarghaoui, Moussa Khouakhi & Mohamed Masmodi
Generalized Krätzel functions: an analytic study
Ashik A. Kabeer & Dilip Kumar
Some boundedness results for Riemann-Liouville tempered fractional integralsn
César E. Torres Ledesma, Hernán A. Cuti Gutierrez, Jesús P. Avalos Rodríguez & Willy Zubiaga Vera
Zuomao Yan
Operational matrix based numerical scheme for the solution of time fractional diffusion equations
S. Poojitha & Ashish Awasthi
Nehari manifold approach for fractional Kirchhoff problems with extremal value of the parameter
Pawan Kumar Mishra & Vinayak Mani Tripathi
Pointwise characterizations of variable Besov and Triebel-Lizorkin spaces via Hajłasz gradients
Yu He, Qi Sun & Ciqiang Zhuo
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Paper Highlight
A Unified Phenomenological Model Captures Water Equilibrium and Kinetic Processes in Soil
Yong Zhang, Martinus Th. van Genuchten, Dongbao Zhou, Golden J. Zhang, HongGuang Sun
Publication information: Water Resources Research 60(3), March 2024.
https://doi.org/10.1029/2023WR035782
Abstract
Soil water sustains life on Earth, and how to quantify water equilibrium and kinetics in soil remains a challenge for over a century despite significant efforts. For example, various models were proposed to interpret non-Darcian flow in saturated soils, but none of them can capture the full range of non-Darcian flow. To unify the different models into one overall framework and improve them if needed, this technical note proposes a theory based on the tempered stable density (TSD) assumption for the soil-hydraulic property distribution, recognizing that the underlying hydrologic processes all occur in the same, albeit very complex and not measurable at all the relevant scales, soil-water system. The TSD assumption forms a unified fractional-derivative equation (FDE) using subordination. Preliminary applications show that simplified FDEs, with proposed hydrological interpretations and TSD distributed properties, effectively capture core equilibrium and kinetic water processes, spanning non-Darcian flow, water retention, moisture movement, infiltration, and wetting/drying, in the soil-water system with various degrees and scales of system heterogeneity. Model comparisons and evaluations suggest that the TSD may serve as a unified density for the properties of a broad range of soil-water systems, driving multi-rate mass, momentum, and energy equilibrium/kinetic processes often oversimplified by classical models as single-rate processes.
Keywords Points
A tempered stable law with subordination built a unified model governing water equilibrium and kinetics in saturated/unsaturated soils;
Fractional-derivative equations fitted soil-water data sets, such as non-Darcian flow, as well as or better than classical models;
The assumed tempered stable density distribution for soil-hydraulic properties led to multi-rate moisture dynamics
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The nonlinear wave dynamics of the space-time fractional van der Waals equation via three analytical methods
Ali Altalbe; Abdullah A. Zaagan; Ahmet Bekir; Adem Cevikel
Publication information: Physics of Fluids 36, 027140 (2024).
https://doi.org/10.1063/5.0196639
Abstract
In this paper, we explore the new exact soliton solutions of the truncated M-fractional nonlinear (1 + 1)-dimensional van der Waals equation by applying the function method, extended -expansion method, and modified simplest equation method. The concerned equation is a challenging problem in the modeling of molecules and materials. Noncovalent van der Waals or dispersion forces are frequent and have an impact on the structure, dynamics, stability, and function of molecules and materials in biology, chemistry, materials science, and physics. The results obtained are verified and represented by two-dimensional, three-dimensional, and contour graphs. These results are newer than the existing results in the literature due to the use of fractional derivative. The achieved solutions will be of high significance in the interaction of quantum-mechanical fluctuations, granular matter, and other areas of van der Waals equation applications. Therefore, the obtained solutions are valuable for future studies of this model.
Keywords
Equations of state; Wave mechanics; Optical solitons; Soliton solutions; Variational methods; Surface waves
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