FDA Express Vol. 42, No. 2, Feb. 28, 2022
FDA Express Vol. 42, No. 2, Feb. 28, 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.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 42_No 2_2022.pdf
◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Fractional Dynamical Systems: Applications and Theoretical Results
Application of Fractional Calculus as an Interdisciplinary Modeling Framework
◆ Books
Theory and Numerical Approximations of Fractional Integrals and Derivatives
◆ Journals
Computers & Mathematics with Applications
◆ Paper Highlight
The discrete fractional order difference applied to an epidemic model with indirect transmission
Stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise
◆ 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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An analytical solution for the Caputo type generalized fractional evolution equation
By: Sawangtong, W and Sawangtong, P
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Published: JUL 2022
By: Ganesh, A; Deepa, S; etc.
AIMS MATHEMATICS Volume: 7 Page:1791-1810 Published: 2022
By: Abdelkawy, MA; Amin, AZM; etc.
FRACTAL AND FRACTIONAL Volume: 6 Published: Jan 2022
By: Wang, J; Wang, JQ; etc.
EXPERT SYSTEMS WITH APPLICATIONS Volume: 192 Published: Apr 15 2022
By: Subramanian, M; Manigandan, M; etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 16 Page:1-23 Published: Dec 31 2022
By: Koprulu, MO
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 16 Page: 66-74 Published: Dec 31 2022
By:Ma, YK; Kavitha, K; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume:61 Page: 7291-7302 Published: Sep 2022
By: Zubair, T; Lu, T; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page: 5269-5281 Published: Jul 2022
An analytical solution for the Caputo type generalized fractional evolution equation
By: Sawangtong, W and Sawangtong, P
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page: 5475-5483 Published: Jul 2022
A robust study of a piecewise fractional order COVID-19 mathematical model
By: Zeb, A; Atangana, A; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page: 5649-5665 Published: Jul 2022
By:Berredjem, N; Maayah, B and Abu Arqub, O
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page: 5699-5711 Published: Jul 2022
By: Ahmad, S; Ullah, A; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page: 5735-5752 Published: Jul 2022
By:Abu Arqub, O; Al-Smadi, M; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page: 5753-5769 Published: Jul 2022
On a discrete composition of the fractional integral and Caputo derivative
By:Plociniczak, L
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 108 Published: MAY 2022
By: Ma, ZQ; Liu, ZX; etc.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Volume: 69 Page: 5165-5174 Published: May 2022
By: Ge, QW; Kou, BQ; etc.
IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS Volume: 69 Page: 5018-5029 Published: May 2022
Compact implicit difference approximation for time-fractional diffusion-wave equation
By:Ali, U; Iqbal, A; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page:4119-4126 Published: May 2022 |
By:Yousri, D; AbdelAty, AM; etc.
EXPERT SYSTEMS WITH APPLICATIONS Volume: 192 Published: Apr 15 2022
By: Sahlan, MN and Afshari, H
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 107 Published: Apr 2022
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Call for Papers
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Fractional Dynamical Systems: Applications and Theoretical Results
( A special issue of Fractal and Fractional )
Dear Colleagues: The fractional dynamic is a field of study in mathematics and physics that investigates the behavior of objects and systems by using differentiations of fractional orders. Due to its widespread applications in science and technology, research within the fractional dynamical systems has led to new developments that have attracted the attention of a considerable audience of professionals such as mathematicians, physicists, applied researchers and practitioners. Unlike integer-order models, fractional-order models have the potential to capture nonlocal relations in time and space with power law memory kernels. This means that they provide more realistic and adequate descriptions for many real-world phenomena. In spite of the tremendous amount of published results focused on fractional differential equations and dynamical systems, we believe that many challenging open problems remain. Indeed, the theory and application of these systems are still very active areas of research.
The main objective of this Special Issue is to fill a void in the literature by making relevant information available for an important area of research. The Special Issue on “Fractional Dynamical Systems: Applications and Theoretical Results” provides an international forum for researchers to contribute with original research focusing on the latest achievements in the theory and application of fractional dynamical systems.
Keywords:
- Fractional differential/difference equations
- Fractional stability and control
- Fractional Oscillation and boundedness
- Fractional chaos and bifurcation
- Fractional iterative methods and numerical computations
- Fractional modelling and simulation
- Fractional inequalities
- Fractional stochastic analysis
Organizers:
Prof. Dr. Jehad Alzabut
Prof. Dr. Shahram Rezapour
Prof. Dr. George M. Selvam
Guest Editors
Important Dates:
Deadline for manuscript submissions: 20 March 2022.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/fractional_dynamical_systems.
Application of Fractional Calculus as an Interdisciplinary Modeling Framework
( A special issue of Fractal and Fractional )
Dear Colleagues: From a mathematical fantasy to a complex and rigorous mathematical theory, the subject of fractional calculus has applications in diverse and widespread fields of engineering and science, having a rapid growth of its applications.
One of the greatest ways to make discoveries in math and science is finding answers to many new questions and interesting results. Even if fractional calculus has found an important place in science and engineering as a powerful tool for modeling complex phenomena with many excellent results, there are still some unresolved challenges.
The aim of this special issue is to bring together researchers of diverse fields of Physics, Medicine, Biology, Biosciences, Engineering, Robotics and Signal Processing, including Applied Mathematics and to create an international and interdisciplinary framework for sharing innovative research work related to fractional calculus.
This special issue will cover all theoretical and applied aspects of the fractional calculus and related approaches. Original research articles submissions dealing with topics mentioned bellow are encourage.
Topics:
- Fractional Differential Theory and Application
- Fractional Differential Equation Numerical Solution and Application
- Fractional Integral Theory and Application
- Fractional Integral Equation Numerical Solution and Application
- Local Fractional Calculus Theory and Application
Applications of fractional differentiation in signal analysis, chaos, bioengineering, economics, finance, fractal theory, optics, control systems, artificial intelligence, mathematical biology, nanotechnology and medicine, physics, mechanics, engineering, probability and statistics.
Keywords:
- general fractional calculus
- special functions
- integral transforms
- harmonic analysis
- fractional variational calculus
- ODEs, PDEs and integral equations and systems
- wave equation
- evolution equation
- mathematical models of phenomena
- fractional quantum fields
- nonlinear control methods
- fractional-order controllers
- bio-medical applications
- economic models with memory
- numerical and approximation methods
- computational procedures and algorithms
Organizers:
Dr. Antonela Toma
Prof. Dr. Dorota Mozyrska
Dr. Octavian Postavaru
Dr. Mihai Rebenciuc
Dr. Simona Mihaela Bibic
Guest Editor
Important Dates:
Deadline for manuscript submissions: 24 April 2022.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/fract_calc_model.
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Books
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Theory and Numerical Approximations of Fractional Integrals and Derivatives
( Authors: Changpin Li and Min Cai )
Details: https://doi.org/10.1137/1.9781611975888
Book Description:
Due to its ubiquity across a variety of fields in science and engineering, fractional calculus has gained momentum in industry and academia. While a number of books and papers introduce either fractional calculus or numerical approximations, no current literature provides a comprehensive collection of both topics. This monograph introduces fundamental information on fractional calculus and provides a detailed treatment of existing numerical approximations.
Theory and Numerical Approximations of Fractional Integrals and Derivatives presents an inclusive review of fractional calculus in terms of theory and numerical methods and systematically examines almost all existing numerical approximations for fractional integrals and derivatives. The authors consider the relationship between the fractional Laplacian and the Riesz derivative, a key component absent from other related texts, and highlight recent developments, including their own research and results.
The book's core audience spans several fractional communities, including those interested in fractional partial differential equations, the fractional Laplacian, and applied and computational mathematics. Advanced undergraduate and graduate students will find the material suitable as a primary or supplementary resource for their studies.
Author Biography:
Changpin Li, full Professor of Mathematics, Shanghai University. Main interests: 1) Applied theory and computation of bifurcation and chaos 2) Numerical methods for fractional partial differential equations.
Min Cai, Shanghai University.
Contents:
Front Matter
Fractional integrals
Riemann-Liouville integral; Fractional integrals of other types;
Fractional derivatives
Riemann-Liouville derivative; Some remarks on the Riemann-Liouville derivative; Caputo derivative; Some remarks on the Caputo derivative; Riesz derivative; The fractional Laplacian; Fractional derivatives of other types; Definite conditions for fractional differential equations;
Numerical fractional integration
Numerical methods based on polynomial interpolation; Fractional linear multistep method; Spectral approximations; Diffusive approximation;
Numerical Caputo differentiation
L1, L2, and L2C methods; High-order methods based on polynomial interpolation; Fractional linear multistep method; Spectral approximations; Diffusive approximation;
Numerical Riemann-Liouville differentiation
L1, L2, and L2C methods; Approximation based on spline interpolation; Grünwald-Letnikov type approximations; Fractional backward difference formulae with modifications;Fractional average central difference method; Spectral approximations; Numerical method based on finite-part integrals;
Numerical Riesz differentiation
Indirect approximations to the fractional diffusion operator; Direct approximations to the fractional diffusion operator; Indirect approximations to the fractional convection operator; Direct approximations to the fractional convection operator;
Numerical fractional Laplacian
Approximations based on regularization and interpolation; Approximation based on the weighted trapezoidal rule; Some remarks on the numerical fractional Laplacian;
Back Matter
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Journals
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Computers & Mathematics with Applications
(Selected)
Yuehua Jiang, HongGuang Sun, Yu Bai, Yan Zhang
Daxin Nie, Weihua Deng
Lei Zhang, Guo-Feng Zhang, Zhao-Zheng Liang
Yadong Zhang, Minfu Feng
A fast finite volume method for spatial fractional diffusion equations on nonuniform meshes
Zhi-Wei Fang, Jia-Li Zhang, Hai-Wei Sun
A high-order scheme for time-space fractional diffusion equations with Caputo-Riesz derivatives
Golsa Sayyar, Seyed Mohammad Hosseini, Farinaz Mostajeran
Mengchen Zhang, Fawang Liu, Ian W.Turner, Vo V.Anh, Libo Feng
Fast image inpainting strategy based on the space-fractional modified Cahn-Hilliard equations
Min Zhang, Guo-Feng Zhang
Shengyue Li, Wanrong Cao, Yibo Wang
Radial point interpolation collocation method based approximation for 2D fractional equation models
Qingxia Liu, Pinghui Zhuang, Fawang Liu, Minling Zheng, Shanzhen Chen
Yue Wang, Hu Chen
Li Chai, Yang Liu, Hong Li
Xuehua Yang, Wenlin Qiu, Haixiang Zhang, Liang Tang
An optimization-based approach to parameter learning for fractional type nonlocal models
Olena Burkovska, Christian Glusa, Marta D'Elia
Dongdong Hu, Yuezheng Gong, Yushun Wang
(Selected)
A note on stability of fractional logistic maps
Jessica Mendiola-Fuentes, Daniel Melchor-Aguilar
The proof of Lyapunov asymptotic stability theorems for Caputo fractional order systems
Yiheng Wei, Jinde Cao, Yuquan Chen, Yingdong Wei
Caputo–Hadamard fractional Halanay inequality
Bin-Bin He, Hua-Cheng Zhou
A reproducing kernel method for nonlinear C-q-fractional IVPs
YueYu Jing, NiuJian Zhang, Siyu Ning
A novel adaptive Crank–Nicolson-type scheme for the time fractional Allen–Cahn model
Shuangjian Guo, Jincheng Ren
Efficient approach to solve time fractional Kardar–Parisi–Zhang equation on unbounded domains
Yuchen Wu, Hongwei Li
An optimal and low computational cost fractional Newton-type method for solving nonlinear equations
Giro Candelario, Alicia Cordero, Juan R.Torregrosa, María P.Vassileva
Solution of a fractional logistic ordinary differential equation
Juan J. Nieto
A strong maximum principle for the fractional (p,q)-Laplacian operator
Vincenzo Ambrosio
Semi-discretized numerical solution for time fractional convection–diffusion equation by RBF-FD
Juan Liu, Juan Zhang, Xindong Zhang
Analysis of a hidden memory variably distributed-order space-fractional diffusion equation
Jinhong Jia, Hong Wang
A high-precision numerical approach to solving space fractional Gray-Scott model
Che Han, Yu-Lan Wang, Zhi-Yuan Li
α-robust H1-norm error estimate of nonuniform Alikhanov scheme for fractional sub-diffusion equation
Hu Chen, Yue Wang, Hongfei Fu
Leijie Qiao, Bo Tang
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Paper Highlight
The discrete fractional order difference applied to an epidemic model with indirect transmission Carmen Coll, Alicia Herrero, Damián Ginestar, Elena Sánchez
Publication information: Applied Mathematical Modelling: Volume 103, March 2022
https://doi.org/10.1016/j.apm.2021.11.002
Abstract
A discrete fractional order model is proposed to analyze the behaviour of an epidemic process with indirect transmission. This model is based on a discrete version of the GrunwaldLetnikov fractional derivative operator. Some properties of this operator are shown and used to derive a truncated version of the operator, which is used to propose a model with short-term memory. Based on the biological meaning of the problem, some bounds have been obtained to assure the nonnegativity of the model solution. The (α, k)-Basic Reproduction Number has been introduced and used to analyze the stability of the solution around its equilibrium points. Moreover, the influence of the fractional order, α, and the memory steps, k, on the behaviour of the solution has been analyzed. Finally, the results obtained have been clarified by means of numerical simulations of a model for the evolution of an infection by Salmonella in a hens farm.
Keywords
Epidemic process; Discrete fractional-order; Indirect transmission; Stability
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Dongliang Hu, Yong Huang
Stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise
Publication information: Nonlinear Dynamics: Published February 2022
https://doi.org/10.1007/s11071-022-07278-w
Abstract
In this paper, the moment Lyapunov exponent and stochastic stability of a fractional viscoelastic plate driven by non-Gaussian colored noise is investigated. Firstly, the stochastic dynamic equations with two degrees of freedom are established by piston theory and Galerkin approximate method. The fractional Kelvin–Voigt constitutive relation is used to describe the material properties of the viscoelastic plate, which leads to that the fractional derivation term is introduced into the stochastic dynamic equations. And the noise is simplified into an Ornstein–Uhlenbeck process by utilizing the pathintegral method. Then, via the singular perturbation method, the approximate expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulations. Finally, the effects of the noise, viscoelastic parameters and system parameters on the stochastic dynamics of the viscoelastic plate are discussed.
Keywords:
Stochastic stability; Moment Lyapunov exponent; Largest Lyapunov exponent; Perturbation method; Monte Carlo simulation; Fractional order calculus
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