FDA Express Vol. 36, No. 2, Aug 30, 2020
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Editors: http://jsstam.org.cn/fda/Editors.htm
Institute of Soft Matter Mechanics, Hohai
University
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shuhong@hhu.edu.cn,
fdaexpress@hhu.edu.com
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◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Dynamical Systems, Differential Equations and Applications
◆ Books
Fractional Calculus in Medical and Health Science
◆ Journals
Advances in Nonlinear Analysis
◆ Paper Highlight
Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators
◆ 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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Optimal leader-following consensus of fractional opinion formation models
By: Almeida, Ricardo; Kamocki, Rafal; Malinowska, Agnieszka B.; etc..
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 381 Published: JAN 1 2021
Robust stability criterion for perturbed singular systems of linearized differential equations
Option pricing in illiquid markets: A fractional jump-diffusion approach
Some comments on using fractional derivative operators in modeling non-local diffusion processes
Solving ill-posed problems faster using fractional-order Hopfield neural network
Euler-Maruyama scheme for Caputo stochastic fractional differential equations
Shifted Jacobi spectral-Galerkin method for solving fractional order initial value problems
Semi-Linear Fractional sigma-Evolution Equations with Nonlinear Memory
A Weak Galerkin Finite Element Method for High Dimensional Time-fractional Diffusion Equation
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Call for Papers
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(research topic of Frontiers)
As an extension of the classical integer-order modeling approach, fractional calculus has long been recognized as an efficient and valuable tool in modeling complex phenomena, such as anomalous diffusion, viscoelastic behaviors, heat conduction, chaos, and magnetic resonance imaging. Nowadays, various numerical methods also have been conducted to reveal the underground physical interpretations for the fractional models. Nevertheless, the fractional operator is well-known as a non-local one, which will bring in remarkable computational costs and memory requirements for the numerical simulation.
Hausdorff fractal derivative, one kind of fractal derivatives, has also been proposed to describe a variety of complex problems. Fractal operator significantly extends the application scope of the classical calculus modeling approach under the framework of continuum mechanics to fractal materials. The Hausdorff derivative is mathematically simple and numerically easy to implement with clear physical significance and real-world applications.
Nowadays, various modeling formalisms, including fractional derivative and Hausdorff fractal derivative operators, have been proposed to characterize anomalous physical and engineering behaviors. The fractional derivative operator is well suitable for non-local phenomena and long-term interactions, while Hausdorff fractal derivative underlines the Non-Euclidean distance and temporal scale effect. The inherent relationships and comparisons between these models lack detailed discussions.
Moreover, the existing models have been found to well describe some specific problems with data fitting or qualitative analysis. The underlying physical interpretations of the modeling formalisms or identifications of parameters still require intensive attention.
This Research Topic aims to collect the up-to-the-minute developments in such two modeling operators, including modeling and numerical simulation.
Related research areas (not limited to):
• Anomalous diffusion: ultra-slow diffusion, sub- and super diffusion;Important Note:
All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.Submission Deadlines:
Submission of Abstract: 15 November 2020
Submission of Manuscript: 13 January 2021
All details on this online conference are now available at: https://www.frontiersin.org/research-topics/15439/applications-of-fractional-and-hausdorff-fractal-derivatives-in-modeling-of-anomalous-physical-and-e.
Dynamical Systems, Differential Equations and Applications
(special issue of entropy)
This Special Issue is dedicated to the International Conference on Mathematical Analysis and Applications in Science and Engineering (ICMA2SC’20, https://www.isep.ipp.pt/Page/ViewPage/ICMASC). ICMA2SC’20 is a refereed conference emphasizing different topics of mathematical analysis and applications in science and engineering. This Special Issue will focus on dynamical systems taken in the broad sense; these include, in particular, iterative dynamics, ordinary differential equations, and (evolutionary) partial differential equations. We welcome papers dealing with these topics, either at a theoretical level or at a level of their multiple applications to physics (e.g., cosmology, quantum physics and matter theory, and thermodynamics), or yet as standard applications to control theory, artificial intelligence, diagnosis algorithms, and so on.
Entropy is an international journal enjoying a high Impact Factor, and definitely constitutes one of the most appropriate outlets for the publication of quality research in the topics mentioned above. Note that both original research works and outstanding review articles are called for in this Special Issue.
Keywords:
- iterative dynamicsManuscript Submission Information:
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.Submission Deadlines:
The official submission deadline is 1 October 2020 and will be *postponed* to 2021 year at a later stage.
All details on this online conference are now available at: https://www.mdpi.com/journal/entropy/special_issues/diff.
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Books
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(Editors:Devendra Kumar, Jagdev Singh )
Book Description
This book covers applications of fractional calculus used for medical and health science. It offers a collection of research articles built into chapters on classical and modern dynamical systems formulated by fractional differential equations describing human diseases and how to control them.
The mathematical results included in the book will be helpful to mathematicians and doctors by enabling them to explain real-life problems accurately. The book will also offer case studies of real-life situations with an emphasis on describing the mathematical results and showing how to apply the results to medical and health science, and at the same time highlighting modeling strategies.
The book will be useful to graduate level students, educators and researchers interested in mathematics and medical science.
Editors Biography
Devendra Kumar is an Assistant Professor in the Department of Mathematics, University of Rajasthan, Jaipur-302004, Rajasthan, India. He did his Master of Science (M.Sc.) in Mathematics and Ph.D. in Mathematics from University of Rajasthan, India. He primarily teaches the subjects like real and complex analysis, functional analysis, integral equations and special functions in post-graduate level course in mathematics. His area of interest is Mathematical Modelling, Special Functions, Fractional Calculus, Applied Functional Analysis, Nonlinear Dynamics, Analytical and Numerical Methods. He has published two books: Engineering Mathematics-I (2008), Engineering Mathematics-II (2013). His works have been published in the Nonlinear Dynamics, Chaos Solutions & Fractals, Physical A, Journal of Computational and Nonlinear Dynamics, Applied Mathematical Modelling, Entropy, Advances in Nonlinear Analysis, Romanian Reports in Physics, Applied Mathematics and Computation, Chaos and several other peer-reviewed international journals. His 130 research papers have been published in various Journals of repute with h-index of 30. He has attained a number of National and International Conferences and presented several research papers. He has also attended Summer Courses, Short Terms Programs and Workshops.
Jagdev Singh is an Associate Professor in the Department of Mathematics, JECRC University, Jaipur-303905, Rajasthan, India. He did his Master of Science (M.Sc.) in Mathematics and Ph.D. in Mathematics from University of Rajasthan, India. He primarily teaches the subjects like mathematical modeling, real analysis, functional analysis, integral equations and special functions in post-graduate level course in mathematics. His area of interest is Mathematical Modelling, Mathematical Biology, Fluid Dynamics, Special Functions, Fractional Calculus, Applied Functional Analysis, Nonlinear Dynamics, Analytical and Numerical Methods. He has published three books: Advance Engineering Mathematics (2007), Engineering Mathematics-I (2008), Engineering Mathematics-II (2013). His works have been published in the Nonlinear Dynamics, Chaos Solutions & Fractals, Physica A, Journal of Computational and Nonlinear Dynamics, Applied Mathematical Modelling, Entropy, Advances in Nonlinear Analysis, Romanian Reports in Physics, Applied Mathematics and Computation, Chaos and several other peer-reviewed international journals. His 120 research papers have been published in various Journals of repute with h-index of 30. He has attained a number of National and International Conferences and presented several research papers. He has also attended Summer Courses, Short Terms Programs and Workshops.
Contents:
-Image edge detection using fractional conformable derivatives in Liouville-Caputo sense for medical image processing
J.E. Lavín-Delgado, J.E. Solís-Pérez, J.F. Gómez-Aguilar and R.F. Escobar-Jiménez
-WHO child growth standards modelling by variable-, fractional-order difference equation
Piotr Ostalczyk
-Fractional Calculus Approach in SIRS-SI Model for Malaria Disease with Mittag-Leffler Law
Jagdev Singh, Sunil Dutt Purohit and Devendra Kumar
-Mathematical modelling and analysis of fractional epidemic models using derivative with exponential kernel
Kolade M. Owolabi and Abdon Atangana
-Fractional order mathematical model for cell cycle of tumour cell
Ritu Agarwal, Kritika and S. D. Purohit
-Fractional Order Model of Transmission Dynamics of HIV/AIDS with Effect of Weak CD4+ T-cells
Ved Prakash Dubey, Rajnesh Kumar and Devendra Kumar
-Fractional dynamics of HIV-AIDS and cryptosporidiosis with lognormal distribution
M.A. Khan and Abdon Atangana
-A Fractional Mathematical Model to Study the Effect of Buffer and Endoplasmic Reticulum on Cytosolic Calcium Concentration in Nerve Cells
Brajesh Kumar Jha and Hardik Joshi
-Fractional SIR epidemic model of childhood disease with Mittag-Leffler memory
P. Veeresha, D. G. Prakasha and Devendra Kumar
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Journals
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(Selected)
Samiha Belmor, F. Jarad, T. Abdeljawad, Manar A. Alqudah
Kang-Le Wang, Kang-Jia Wang, Chun-Hui He
Kashif Ali Abro, Ilyas Khan, Kottakkaran Sooppy Nisar
Analysis of dengue fever outbreak by generalized fractional derivative
Paul Bosch, J. F. Gómez-Aguilar, José M. Rodríguez, José M. Sigarreta
A general comparison principle for caputo fractional-order ordinary differential equations
Cong Wu
Some remarks on fractional integral of one-dimensional continuous functions
Jia Yao, Ying Chen, Junqiao Li, Bin Wang
Fractional-order passivity-based adaptive controller for a robot manipulator type scara
J. E. Lavín-Delgado, S. Chávez-Vázquez, J. F. Gómez-Aguilar, G. Delgado-Reyes, M. A. Ruíz-Jaimes
Approximate solution to fractional riccati differential equations
Madiha Gohar
Mathematical analysis of coupled systems with fractional order boundary conditions
Zeeshan Ali, Kamal Shah, Akbar Zada, Poom Kumam
Mathematical and statistical analysis of rl and rc fractional-order circuits
Nadeem Ahmad Sheikh, Dennis Ling Chuan Ching, Sami Ullah, Ilyas Khan
On a high-pass filter described by local fractional derivative
Kang-Jia Wang
Newton’s-type integral inequalities via local fractional integrals
Sabah Iftikhar, Poom Kumam, Samet Erden
On the new explicit solutions of the fractional nonlinear space-time nuclear model
Abdel-Haleem Abdel-Aty, Mostafa M. A. Khater, Raghda A. M. Attia, M. Abdel-Aty, Hichem Eleuch
Shaher Momani, Omar Abu Arqub, Banan Maayah
Fractal dimension of fractional brownian motion based on random sets
Ruishuai Chai
New generalizations in the sense of the weighted non-singular fractional integral operator
Saima Rashid, Zakia Hammouch, Dumitru Baleanu, Yu-Ming Chu
Advances in Nonlinear Analysis
(Selected)
Liouville property of fractional Lane-Emden equation in general unbounded domain
Ying Wang and Yuanhong Wei
Multiple solutions for critical Choquard-Kirchhoff type equations
Sihua Liang, Patrizia Pucci, and Binlin Zhang
Jialin Wang, Maochun Zhu, Shujin Gao, and Dongni Liao
On variational nonlinear equations with monotone operators
Marek Galewski
Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations
Hans-Christoph Grunau, Nobuhito Miyake, and Shinya Okabe
Feng Binhua, Ruipeng Chen, and Jiayin Liu
Global existence and finite time blowup for a nonlocal semilinear pseudo-parabolic equation
Xingchang Wang and Runzhang Xu
Gradient estimate of a variable power for nonlinear elliptic equations with Orlicz growth
Shuang Liang and Shenzhou Zheng
Nehari-type ground state solutions for a Choquard equation with doubly critical exponents
Sitong Chen, Xianhua Tang, and Jiuyang Wei
On isolated singularities of Kirchhoff equations
Huyuan Chen, Mouhamed Moustapha Fall, and Binling Zhang
Multiplicity of concentrating solutions for a class of magnetic Schrödinger-Poisson type equation
Yueli Liu, Xu Li, and Chao Ji
Menglan Liao, Qiang Liu, and Hailong Ye
Optimal rearrangement problem and normalized obstacle problem in the fractional setting
Julián Fernández Bonder, Zhiwei Cheng, and Hayk Mikayelyan
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Paper
Highlight
A. G. Cunha-FilhoY. BriendA. M. G. de LimaM. V. Donadon
Publication information: Mechanical Systems and Signal Processings, Published 1 January 2021
https://doi.org/10.1016/j.ymssp.2020.107042
Abstract
In the open literature, many authors have used the fractional calculus in conjunction with the finite element method to model certain viscoelastic systems. The so-named fractional derivative model may be a better option for transient analyses of systems containing viscoelastic materials due to its causal behavior and its capability to fit accurately the viscoelastic damping properties and to represent properly their fading memory. However, depending on the situation, it leads to costly computations due to the integration of the non-local viscoelastic displacement and stress fields, especially for long time intervals. In this contribution, it is proposed a new and efficient general three-dimensional fractional constitutive formulation based on the use of a recurrence term to give a simplest and low-cost constitutive law to describe the frequency- and temperature-dependent behavior of viscoelastic materials, especially for complex systems. To demonstrate the efficiency and accuracy of the proposed formulation compared with those available in the literature, an academic example formed by a thin three-layer sandwich plate is performed and the main features and capabilities of the proposed methodology are highlighted.
Highlights:
• A general three-dimensional constitutive equation based on the fractional calculus.
• Use of the fractional derivative model (FDM) for viscoelastic systems.
• An efficient and accurate new FDM formulation based on a recurrence term.
• Eliminate the self-dependency of the viscoelastic stress field of the constitutive equation.
• Verification of the proposed new formulation with those available in the open literature.
Keywords:
Viscoelasticity; Fractional derivative model; Recurrence termFinite element
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Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators
Renat T. Sibatov, HongGuang Sun
Publication information: Fractal Fract, Volume 4, Issue 3, 2020
https://doi.org/10.3390/fractalfract4030042
Abstract
The approach based on fractional advection–diffusion equations provides an effective and meaningful tool to describe the dispersive transport of charge carriers in disordered semiconductors. A fractional generalization of Fick’s law containing the Riemann–Liouville fractional derivative is related to the well-known fractional Fokker–Planck equation, and it is consistent with the universal characteristics of dispersive transport observed in the time-of-flight experiment (ToF). In the present paper, we consider the generalized Fick laws containing other forms of fractional time operators with singular and non-singular kernels and find out features of ToF transient currents that can indicate the presence of such fractional dynamics. Solutions of the corresponding fractional Fokker–Planck equations are expressed through solutions of integer-order equation in terms of an integral with the subordinating function. This representation is used to calculate the ToF transient current curves. The physical reasons leading to the considered fractional generalizations are elucidated and discussed.
Keywords:
anomalous diffusion; fractional equation; dispersive transport; time-of-flight experiment
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The End of This Issue
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