FDA Express Vol. 31, No. 1, April 30, 2019
All issues: http://jsstam.org.cn/fda/
Editors: http://jsstam.org.cn/fda/Editors.htm
Institute of Soft Matter Mechanics, Hohai University
For contribution: suxianglong1303@hhu.edu.cn, fdaexpress@hhu.edu.com
For subscription:
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◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Training school on Computational Methods for Fractional-Order Problems
◆ Books
HAUSDORFF CALCULUS: Applications to Fractal Systems
◆ Journals
◆ Paper Highlight
Can we split fractional derivative while analyzing fractional differential equations?
Inverse Mittag-Leffler stability of structural derivative nonlinear dynamical systems
◆ 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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Fractional Integration and Fat Tails for Realized Covariance Kernels
By: Opschoor, Anne; Lucas, Andre
JOURNAL OF FINANCIAL ECONOMETRICS Volume: 17 Issue: 1 Pages: 66-90 Published:
WIN 2019
Analytical and numerical solutions of a multi-term time-fractional Burgers'
fluid model
By: Zhang, Jinghua; Liu, Fawang; Lin, Zeng; etc.
APPLIED MATHEMATICS AND COMPUTATION Volume: 356 Pages: 1-12 Published: SEP 1
2019
An alternating direction implicit scheme of a fractional-order diffusion tensor
image registration model
By: Han, Huan; Wang, Zhanqing
APPLIED MATHEMATICS AND COMPUTATION Volume: 356 Pages: 105-118 Published: SEP 1
2019
Properties and distribution of the dynamical functional for the fractional
Gaussian noise
By: Loch-Olszewska, Hanna
APPLIED MATHEMATICS AND COMPUTATION Volume: 356 Pages: 252-271 Published: SEP 1
2019
Haar wavelet method for approximating the solution of a coupled system of
fractional-order integral-differential equations
By: Xie, Jiaquan; Wang, Tao; Ren, Zhongkai; etc.
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 163 Pages: 80-89 Published: SEP
2019
Necessary and sufficient conditions for the dynamic output feedback
stabilization of fractional-order systems with order 0 < alpha < 1
By: Guo, Ying; Lin, Chong; Chen, Bing; etc.
SCIENCE CHINA-INFORMATION SCIENCES Volume: 62 Issue: 9 Document number: 199201
Published: SEP 2019
DYNAMICS OF NON-AUTONOMOUS FRACTIONAL STOCHASTIC GINZBURG-LANDAU EQUATIONS WITH
MULTIPLICATIVE NOISE
By: Lan, Yun; Shu, Ji
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume: 18 Issue: 5 Pages: 2409-2431
Published: SEP 2019
GLOBAL ASYMPTOTIC STABILITY OF TRAVELING WAVES TO THE ALLEN-CAHN EQUATION WITH A
FRACTIONAL LAPLACIAN
By: Ma, Luyi; Niu, Hong-Tao; Wang, Zhi-Cheng
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume: 18 Issue: 5 Pages: 2457-2472
Published: SEP 2019
EXISTENCE, UNIQUENESS AND REGULARITY OF THE SOLUTION OF THE TIME-FRACTIONAL
FOKKER PLANCK EQUATION WITH GENERAL FORCING
By: Le, Kim-Ngan; Mclean, William; Stynes, Martin
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume: 18 Issue: 5 Pages: 2789-2811
Published: SEP 2019
GROUND STATE SOLUTIONS FOR FRACTIONAL SCALAR FIELD EQUATIONS UNDER A GENERAL
CRITICAL NONLINEARITY
By: Alves, Claudianor O.; Figueiredo, Giovany M.; Siciliano, Gaetano
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume: 18 Issue: 5 Pages: 2199-2215
Published: SEP 2019
Mean-field anticipated BSDEs driven by fractional Brownian motion and related
stochastic control problem
By: Douissi, Soukaina; Wen, Jiaqiang; Shi, Yufeng
APPLIED MATHEMATICS AND COMPUTATION Volume: 355 Pages: 282-298 Published: AUG 15
2019
Finite element simulation and efficient algorithm for fractional Cahn-Hilliard
equation
By: Wang, Feng; Chen, Huanzhen; Wang, Hong
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 356 Pages: 248-266
Published: AUG 15 2019
Error estimate of finite element/finite difference technique for solution of
two-dimensional weakly singular integro-partial differential equation with space
and time fractional derivatives
By: Dehghan, Mehdi; Abbaszadeh, Mostafa
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 356 Pages: 314-328
Published: AUG 15 2019
Well-posedness and EM approximations for non-Lipschitz stochastic fractional
integro-differential equations
By: Dai, Xinjie; Bu, Weiping; Xiao, Aiguo
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 356 Pages: 377-390
Published: AUG
15 2019
A robust kernel-based solver for variable-order time fractional PDEs under 2D/3D
irregular domains
By: Fu, Zhuo-Jia; Reutskiy, Sergiy; Sun, Hong-Guang; etc.
APPLIED MATHEMATICS LETTERS Volume: 94 Pages: 105-111 Published: AUG 2019
On the solutions of (2+1)-dimensional time-fractional Schrodinger equation
By: Li, Chao; Guo, Qilong; Zhao, Meimei
APPLIED MATHEMATICS LETTERS Volume: 94 Pages: 238-243 Published: AUG 2019
Regularity properties of the solution to a stochastic heat equation driven by a
fractional Gaussian noise on S-2
By: Lan, Xiaohong; Xiao, Yimin
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 476 Issue: 1 Pages:
27-52 Published: AUG 1 2019
A new computational method based on optimization scheme for solving
variable-order time fractional Burgers' equation
By: Hassani, Hossein; Naraghirad, Eskandar
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 162 Pages: 1-17 Published: AUG
2019
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Call for Papers
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Training school on
Computational Methods for Fractional-Order Problems
(Bari (Italy), July 22-26 2019)
A training school on Computational Methods for Fractional-Order Problems will be
held in Bari (Italy) on July 22-26 2019.
The aim of the Training School is to provide to young researchers and PhD
students the background for understanding the mathematics beyond operators of
non-integer order and devise accurate and reliable computational methods. In
particular, the development of numerical software for the effective treatment of
fractional differential equations will be one of the main assets of the training
school with the possibility of organizing some laboratory tutorials.
The Training School is an activity of the Cost Action CA 15225 Fractional
Systems and there is no admission fee but the number of places is limited. Some
grants to support the participation from European countries are available.
Lecturers of the school will be: Kai Diethelm (Germany), Roberto Garrappa
(Italy), Guido Maione (Italy) Maria Luisa Morgado (Portugal), Marina Popolizio
(Italy), Magda Stela Rebelo (Portugal), Abner J. Salgado (USA), Martin Stynes
(China), Yubin Yan (UK)
Further information at:
https://fractional-systems.eu/ts-2019/
https://www.dm.uniba.it/Members/garrappa/CA-TS-2019
The deadline for applications is May 25, 2019
Scientific and organizing Committee
prof. Roberto Garrappa (chair)
prof. Kai Diethelm
prof. Paolo Lino
prof. Guido Maione
prof. Tiziano Politi
prof. Marina Popolizio
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Books
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(Editors: Yingjie Liang, Wen Chen, Wei Cai)
Details:
https://www.degruyter.com/view/product/506187#?tdsourcetag=s_pctim_aiomsgIntroduction
This book introduces the fundamental concepts, methods, and applications of Hausdorff calculus, with a focus on its applications in fractal systems. Topics such as the Hausdorff diffusion equation, Hausdorff radial basis function, Hausdorff derivative nonlinear systems, PDE modeling, statistics on fractals, etc. are discussed in detail. It is an essential reference for researchers in mathematics, physics, geomechanics, and mechanics.
-Presents the theory
and applications of Hausdorff calculus.
-Covers applications in dynamics, statistics, mechanics, and computation.
-Of interest to mathematicians and physicists as well as to engineers.
Chapters
-Introduction
-Hausdorff diffusion equation
-Statistics on fractals
-Lyapunov stability of Hausdorff derivative non-linear systems
-Hausdorff radial basis function
-Hausdorff PDE modeling
-Local structural derivative
-Perspectives
The Contents is available at:
https://www.degruyter.com/view/product/506187#?tdsourcetag=s_pctim_aiomsg
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Journals
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(Selected)
Wei Cai; Wen Chen; Jun Fang; Sverre Holm
Yuriy A. Rossikhin; Marina V. Shitikova
Reflections on Two Parallel Ways in the Progress of Fractional Calculus in Mechanics of Solids
Yuriy A. Rossikhin
Luis E. Suárez; Arsalan Shokooh; José Arroyo
Yuriy A. Rossikhin; Marina V. Shitikova
Response of Systems With Damping Materials Modeled Using Fractional Calculus
L. Suarez; A. Shokooh
[Back]
(Selected)
Time-Dependent Decay Rate and Frequency for Free Vibration of Fractional Oscillator
Y. M. Chen; Q. X. Liu; J. K. Liu
Qiang Feng Lü; Mao Lin Deng; Wei Qiu Zhu
Pol D. Spanos; Alberto Di Matteo; Yezeng Cheng; Antonina Pirrotta; Jie Li
Mao Lin Deng; Wei Qiu Zhu
A Modified Fractional Calculus Approach to Model Hysteresis
Mohammed Rabius Sunny; Rakesh K. Kapania; Ronald D. Moffitt; Amitabh Mishra; Nakhiah Goulbourne
N. Gil-Negrete; J. Vinolas; L. Kari
Response of a Helix Made of a Fractional Viscoelastic Material
M. Ostoja-Starzewski; H. Shahsavari
Dynamic Viscoelastic Rod Stability Modeling by Fractional Differential Operator
D. Ingman; J. Suzdalnitsky
S. Saha Ray; B. P. Poddar; R. K. Bera
An Eigenvector Expansion Method for the Solution of Motion Containing Fractional Derivatives
L. E. Suarez; A. Shokooh
On the Appearance of the Fractional Derivative in the Behavior of Real Materials
P. J. Torvik; R. L. Bagley
Applications of Fractional Calculus to the Theory of Viscoelasticity
R. C. Koeller
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Paper Highlight
Can we split fractional derivative while analyzing fractional differential equations?
Guotao Wang, Ke Pei, Ravi P. Agarwal, Lihong Zhang, Bashir Ahmad
Publication information:
Communications in Nonlinear Science and Numerical Simulation, Volume 76, September 2019, Pages 12-24.
Abstract
Fractional derivatives are generalization to classical integer-order
derivatives. The rules which are true for classical derivative need not hold for
the fractional derivatives. For example, it is proved in the literature that we
cannot simply add the fractional orders $\alpha$ and $\beta$ in
$\mathrm{D}^\alpha \mathrm{D}^\beta$ to produce the fractional derivative
$\mathrm{D}^{\alpha+\beta}$ of order $\alpha+\beta$, in general. In this article
we discuss the details of such compositions and propose the conditions to split
a linear fractional differential equation into systems involving lower order
derivatives. We provide some examples, which show that the conditions of the
related results in the literature are sufficient but not necessary. Further, we
point out that the fractional differential equations formed using the
derivatives which satisfy the composition rule $\mathrm{D}^\alpha
\mathrm{D}^\beta=\mathrm{D}^\beta\mathrm{D}^\alpha=\mathrm{D}^{\alpha+\beta}$
produce only a trivial solution.
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Inverse Mittag-Leffler stability of structural derivative nonlinear dynamical
systems
Dongliang Hu, Wen Chen, Yingjie Liang
Publication information:
Chaos, Solitons & Fractals, Volume 123, June 2019, Pages 304-308
Abstract
The logarithmic time evolution is widely observed in laboratory and field measurements. However, logarithmic stability has not been well considered till now. In this paper, the definition of Lyapunov stability, including logarithmic and inverse Mittag-Leffler stabilities, is proposed. And via the Lyapunov direct method, the stability of nonlinear dynamical systems based on the structural derivative is investigated. Furthermore, the comparison principle based on the structural derivative is presented in order to obtain the stability conditions for nonlinear dynamical systems. Finally, two demonstrative examples are given to test the proposed stability concept.
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The End of This Issue
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