FDA Express Vol. 46, No. 1, Jan. 31, 2023

发布时间:2023-01-31 访问量:1855

FDA Express    Vol. 46, No. 1, Jan. 31, 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.cnfda@hhu.edu.cn

For subscription: http://jsstam.org.cn/fda/subscription.htm

PDF download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol 46_No 1_2023.pdf


 

◆  Latest SCI Journal Papers on FDA

(Searched on Jan. 31, 2023)

 

  Call for Papers

ICFC 2023: 17. International Conference on Fractional Calculus

Advances in Fractional Order Derivatives and Their Applications


 

◆  Books

The Variable-Order Fractional Calculus of Variations

 

◆  Journals

Chaos, Solitons & Fractals

Fractional Calculus and Applied Analysis

 

  Paper Highlight


Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy

Characterization of three-dimensional fractional viscoelastic models through complex modulus analysis and polar decomposition

 

  Websites of Interest

Fractal Derivative and Operators and Their Applications

Fractional Calculus & Applied Analysis

 

 

 

 

 

========================================================================

 Latest SCI Journal Papers on FDA

------------------------------------------

(Searched on Jan. 31, 2023)




 A novel fractional order model of SARS-CoV-2 and Cholera disease with real data

By: Oezkoese, F; Habbireeh, R and Senel, MT
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 423 Published: May 15 2023


 Modeling and analysis of monkeypox disease using fractional derivatives

By:Okyere, S and Ackora-Prah, J
RESULTS IN ENGINEERING Volume: 17 Published: Mar 2023



 Fredholm boundary-value problem for the system of fractional differential equations

By: Boichuk, O and Feruk, V
NONLINEAR DYNAMICS Published: ‏ Jan 2023



 A PID controller for synchronization between master-slave neurons in fractional-order of neocortical network model

By:Ghasemi, M; Foroutannia, A and Nikdelfaz, F
JOURNAL OF THEORETICAL BIOLOGY Volume: 556 Published: Jan 7 2023



 Deformable Protein Shape Classification Based on Deep Learning, and the Fractional Fokker-Planck and Kahler-Dirac Equations

By: Paquet, E; Viktor, HL; etc.
IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE Volume: ‏45 Page:391-407 Published: Jan 1 2023



 A three-dimensional fractional visco-hyperelastic model for soft materials

By:Gao, YF; Yin, DS; etc.
JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Volume: 137 Published: ‏ Jan 2023



 Preoperative assessment of microvascular invasion of hepatocellular carcinoma using non-Gaussian diffusion-weighted imaging with a fractional order calculus model: A pilot study

By:Chen, JJ; Guo, YX; etc.
MAGNETIC RESONANCE IMAGING Volume:95 Page:110-117 Published:Jan 2023



 A fractional gradient descent algorithm robust to the initial weights of multilayer perceptron

By:Xie, XT; Pu, YF and Wang, J
NEURAL NETWORKS Volume: 158 Page:154-170 Published: Jan 2023



 Richards's curve induced Banach space valued ordinary and fractional neural network approximation

By: Anastassiou, GA and Karateke, S
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS Volume:117 Published: Jan 2023



 Multiple asymptotical w-periodicity of fractional-order delayed neural networks under state-dependent switching?

By:Ci, JX; Guo, ZY; etc.
NEURAL NETWORKS Volume: 157 Page:11-25 Published: Jan 2023



 A Note on Caputo Fractional Derivative in the Space of Linearly Correlated Fuzzy Numbers

By:Lopes, MM; Santo Pedro, F; etc.
APPLICATIONS OF FUZZY TECHNIQUES Page:113-124 Published: 2023



 The multistep Laplace optimized decomposition method for solving fractional-order coronavirus disease model (COVID-19) via the Caputo fractional approach

By: Maayah, B; Moussaoui, A; etc.
DEMONSTRATIO MATHEMATICA Volume: 55 Page:963-977 Published: Dec 31 2022



 Fractional uncertain differential equations with general memory effects: Existences and alpha-path solutions

By:Luo, C; Wu, GC and Huang, LL
NONLINEAR ANALYSIS-MODELLING AND CONTROL Published: 2023



 A numerical approach for solving a class of two-dimensional variable-order fractional optimal control problems using Gegenbauer operational matrix

By:Soufivand, F; Soltanian, F; etc.
IMA JOURNAL OF MATHEMATICAL CONTROL AND INFORMATION Published: Dec 2022



 Multiple exp-function method to solve the nonlinear space-time fractional partial differential symmetric regularized long wave (SRLW) equation and the (1+1)-dimensional Benjamin-Ono equation

By: Aderyani, SR; Saadati, R; etc.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B Published: Dec 2022



 Natural transform decomposition method for the numerical treatment of the time fractional Burgers-Huxley equation

By:Kanth, ASVR; Aruna, K; etc.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS Published: Dec 2022



 Controllability of damped dynamical systems modelled by Hilfer fractional derivatives

By:Naveen, S; Srilekha, R; etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 16 Page:1254-1263 Published:Dec 31 2022 |



 Oil extraction and crude oil price behavior in the United States: a fractional integration and cointegration analysis

By:Monge, M; Cristobal, E; etc.
ENERGY SOURCES PART B-ECONOMICS PLANNING AND POLICY Volume: 17 Published: Dec 31 2022



 Existence, uniqueness and stability of solutions to fractional backward stochastic differential equations

By:Chen, JH; Ke, SA; etc.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Volume: 30 Page:811-829 Published: Dec 31 2022


 

 

 

[Back]

 

==========================================================================

Call for Papers

------------------------------------------


ICFC 2023: 17. International Conference on Fractional Calculus

( September 16-17, 2023 in Rome, Italy)


Dear Colleagues: International Conference on Fractional Calculus aims to bring together leading academic scientists, researchers and research scholars to exchange and share their experiences and research results on all aspects of Fractional Calculus. It also provides a premier interdisciplinary platform for researchers, practitioners and educators to present and discuss the most recent innovations, trends, and concerns as well as practical challenges encountered and solutions adopted in the fields of Fractional Calculus.

Keywords:

- Fractional differential equations
- Fractional integral equations
- Fractional integro-differential equations
- Fractional integrals and fractional derivatives associated with special functions of mathematical physics
- Inequalities and identities involving fractional integrals and fractional derivatives




Organizers:

Orchidea Maria Lecian, Sapienza University of Rome, Italy
Anilkumar Devarapu, University of North Georgia, United States
Xuezhang Hou, Towson University, United States
Christina Pospisil, University of Salvador, United States
Guest Editors

Important Dates:

Deadline for conference receipts: January 31, 2023

All details on this conference are now available at: https://waset.org/fractional-calculus-conference-in-september-2023-in-rome.



Advances in Fractional Order Derivatives and Their Applications

( A special issue of Fractal and Fractional )


Dear Colleagues: Fractional order derivatives have had a revolutionary impact on the scientific community. Its study has grown in leaps and bounds, from analytical methods to numerical techniques. Consequently, applications of fractional order differential equations are now widespread across every possible area of research.

The focus of this Special Issue is on the advancement of research on fractional order derivatives and their multi-faceted applications. Topics that are invited for submission include (but are not limited to):

Mathematical modeling with fractional order derivatives;
Symmetry analysis of fractional order equations;
Conserved quantities related to fractional order models;
The various solution techniques for fractional order equations;
Special functions that are linked to the solution of fractional order equations;
Software to aid computations and analysis for fractional order derivatives and equations.


Keywords:

- Fractional order derivatives
- Fractional calculus
- Caputo derivatives
- Riemann–Liouville derivatives
- Numerical analysis
- Modeling
- Application




Organizers:

Prof. Dr. Sameerah Jamal
Guest Editors




Important Dates:

Deadline for manuscript submissions: 31 January 2023.

All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/fractional_derivative.





[Back]

 

 

===========================================================================

Books

------------------------------------------

The Variable-Order Fractional Calculus of Variations



( Authors: Ricardo Almeida , Dina Tavares , Delfim F. M. Torres )

Details:https://doi.org/10.1007/978-3-319-94006-9


Book Description:


The Variable-Order Fractional Calculus of Variations is devoted to the study of fractional operators with variable order and, in particular, variational problems involving variable-order operators. This brief presents a new numerical tool for the solution of differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one, an approximation formula is obtained in terms of standard (integer-order) derivatives only. Estimations for the error of the approximations are also provided.

The contributors consider variational problems that may be subject to one or more constraints, where the functional depends on a combined Caputo derivative of variable fractional order. In particular, they establish necessary optimality conditions of Euler–Lagrange type. As the terminal point in the cost integral is free, as is the terminal state, transversality conditions are also obtained.

The Variable-Order Fractional Calculus of Variations is a valuable source of information for researchers in mathematics, physics, engineering, control and optimization; it provides both analytical and numerical methods to deal with variational problems. It is also of interest to academics and postgraduates in these fields, as it solves multiple variational problems subject to one or more constraints in a single brief.


Author Biography:

Ricardo Almeida, Delfim F. M. Torres, Department of Mathematics, University of Aveiro, Aveiro, Portugal
Dina Tavares, Polytechnic Institute of Leiria, Leiria, Portugal

Contents:

Front Matter

Fractional Calculus
Abstract; References;

The Calculus of Variations
Abstract; References;

Expansion Formulas for Fractional Derivatives
Abstract; References;

The Fractional Calculus of Variations
Abstract; References;

Back Matter



[Back]


 

========================================================================

 Journals

------------------------------------------

Chaos, Solitons & Fractals

 (Selected)

 


 Computational analysis of local fractional partial differential equations in realm of fractal calculus

Devendra Kumar, Ved Prakash Dubey, etc.


 Asymptotic synchronization of second-fractional -order fuzzy neural networks with impulsive effects

Qiu Peng,Jigui Jian


 The paradigm of quantum cosmology through Dunkl fractional Laplacian operators and fractal dimensions

Rami Ahmad El-Nabulsi, Waranont Anukool


 An integral boundary fractional model to the world population growth

Om Kalthoum Wanassi, Delfim F. M. Torres


 Effects of the medium fractionality and oscillating potential profiles on the Superarrivals of the Gaussian wave packets

D. Haji TaghiTehrani, M.Solaimani


 Fractional models of falling object with linear and quadratic frictional forces considering Caputo derivative

Mustafa Turkyilmazoglu, Mohamed Altanji


 Probabilistic solutions of fractional differential and partial differential equations and their Monte Carlo simulations

T. Oraby, E. Suazo, H. Arrubla


 Existence and uniqueness results for fractional boundary value problems with multiple orders of fractional derivatives and integrals

Tahar Kherraz, Maamar Benbachir, etc.


 A computational numerical algorithm for thermal characterization of fractional unsteady free convection flow in an open cavity

Muhammad Hamid, Muhammad Usman, etc.


 Determining Lyapunov exponents of fractional-order systems: A general method based on memory principle

Hang Li, Yongjun Shen, etc.


 A study of fractional complex Ginzburg–Landau model with three kinds of fractional operators

Maasoomah Sadaf,Ghazala Akram, etc.


 Solutions of the mobile–immobile advection–dispersion model based on the fractional operators using the Crank–Nicholson difference scheme

Mahmut Modanli, Kerim Karadag, etc.


 A new intervention strategy for an HIV/AIDS transmission by a general fractional modeling and an optimal control approach

Dumitru Baleanu, Manijeh Hasanabadi, etc.


 Parameters and order identification of fractional-order epidemiological systems by Lévy-PSO and its application for the spread of COVID-19

Bing Xie, Fudong Ge


 Exact solutions to fractional pharmacokinetic models using multivariate Mittag-Leffler functions

V.F.Morales-Delgado, M.A.Taneco-Hernández, etc.


[Back]


 

 

Fractional Calculus and Applied Analysis

  ( Volume 26, Issue 1 )

 


 New fractional maximal operators in the theory of martingale Hardy and Lebesgue spaces with variable exponents

Ferenc Weisz


 Prabhakar function of Le Roy type: a set of results in the complex plane

Jordanka Paneva-Konovska


 Multi-parametric Le Roy function

Sergei Rogosin & Maryna Dubatovskaya


 A novel approach to stability analysis of a wide class of irrational linear systems

Vukan Turkulov, Milan R. Rapaić & Rachid Malti


 On removable singular sets for solutions of higher order differential inequalities

A. A. Kon’kov & A. E. Shishkov


 Qualitative properties of solutions to a nonlinear time-space fractional diffusion equation

Meiirkhan B. Borikhanov, Michael Ruzhansky & Berikbol T. Torebek


 Local and global conserved quantities involving generalized operators

Chuan-Jing Song & Yi Zhang


 Existence for a class of time-fractional evolutionary equations with applications involving weakly continuous operator

Biao Zeng


 Reconstruction of pointwise sources in a time-fractional diffusion equation

Mourad Hrizi, Maatoug Hassine & Antonio André Novotny


 Lyapunov stability theorems for ψ-Caputo derivative systems

Bichitra Kumar Lenka & Swaroop Nandan Bora


 Rigidity of phase transitions for the fractional elliptic Gross-Pitaevskii system d

Phuong Le


 Limitations and applications in a fractional Barbalat’s Lemma

Noemi Zeraick Monteiro & Sandro Rodrigues Mazorche


 Abstract fractional inverse source problem of order 0<α<1 in a Banach space

Jie Mei & Miao Li


 Concave-convex critical problems for the spectral fractional laplacian with mixed boundary conditions

Alejandro Ortega


 Oscillation of higher order fractional differential equations

Miroslav Bartušek & Zuzana Došlá


 On the lifting property for the lipschitz spaces Λα with α>0

Vincenzo Ambrosio


 A spectral approach to non-linear weakly singular fractional integro-differential equations

Amin Faghih & Magda Rebelo


 A critical elliptic problem involving exponential and singular nonlinearities

Debajyoti Choudhuri & Kamel Saoudi


 Asymptotically autonomous dynamics for fractional subcritical nonclassical diffusion equations driven by nonlinear colored noise

Fuzhi Li & Mirelson M. Freitas


 Exact solutions and Hyers-Ulam stability of fractional equations with double delays

Yixing Liang, Yang Shi & Zhenbin Fan

 

[Back]

 

 

========================================================================

 Paper Highlight

Equivalence between a time-fractional and an integer-order gradient flow: The memory effect reflected in the energy

Marvin Fritz, Ustim Khristenko and Barbara Wohlmuth  

Publication information: Advances in Nonlinear Analysis, October 6, 2022.

https://doi.org/10.1515/anona-2022-0262


Abstract

Time-fractional partial differential equations are nonlocal-in-time and show an innate memory effect. Previously, examples like the time-fractional Cahn-Hilliard and Fokker-Planck equations have been studied. In this work, we propose a general framework of time-fractional gradient flows and we provide a rigorous analysis of well-posedness using the Faedo-Galerkin approach. Furthermore, we investigate the monotonicity of the energy functional of time-fractional gradient flows. Interestingly, it is still an open problem whether the energy is dissipating in time. This property is essential for integer-order gradient flows and many numerical schemes exploit this steepest descent characterization. We propose an augmented energy functional, which includes the history of the solution. Based on this new energy, we prove the equivalence of a time-fractional gradient flow to an integer-order one. This correlation guarantees the dissipating character of the augmented energy. The state function of the integer-order gradient flow acts on an extended domain similar to the Caffarelli-Silvestre extension for the fractional Laplacian. Additionally, we present a numerical scheme for solving time-fractional gradient flows, which is based on kernel compressing methods and reduces the problem to a system of ordinary differential equations. We illustrate the behavior of the original and augmented energy in the case of the Ginzburg-Landau energy.


Keywords

Energy dissipation; Time-fractional gradient flows; History and augmented energy; Well-posedness of variational form; Memory effect

 

[Back]

 

-------------------------------------


Characterization of three-dimensional fractional viscoelastic models through complex modulus analysis and polar decomposition

  Avradip Ghosh, Avinash Kumar Both, Chin Li Cheung

Publication information: Physics of Fluids 34, 077115 (2022).
https://doi.org/10.1063/5.0097196


 

Abstract

Soft materials such as gels, elastomers, and biological tissues have diverse applications in nature and technology due to their viscoelastic nature. These soft materials often exhibit complex rheology and display elastic and viscous characteristics when undergoing deformation. In recent years, fractional calculus has emerged as a promising tool to explain the viscoelastic behavior of soft materials. Scalar constants are primarily used to quantify viscoelastic elements such as springs and dashpots. However, in three-dimensional (3D) space, not all materials show the same elastic or viscoelastic properties in all directions, especially under elastic/viscoelastic wave propagation (or anisotropy). Though previously reported studies on viscoelastic models have explained a power-law decay of the memory functions, none of them explicitly explained the 3D complex modulus through a matrix notation. In this paper, we present a mathematical formulation that employs tensor algebra and fractional calculus to derive the 3D complex modulus of Kelvin-Voigt, Maxwell, and other arrangements of viscoelastic models. The 3D complex modulus provides information about the elastic wave propagation in a media and can be used to explain anisotropy in different viscoelastic materials. Additionally, an advanced formulation of the moduli can improve the modeling in finite element analysis of 3D viscoelastic materials where discretization is vital for studying media of asymmetric shapes. Finally, we demonstrated a polar decomposition method to visualize viscoelastic tensors using the Green Christoffel tensor and surface plots to represent the degrees of anisotropy and viscoelasticity in the Fourier domain when the medium is probed by a time-harmonic homogeneous plane wave.


Keywords

Mechanical instruments; Hooke's law; Wave propagation; Rheological properties; Viscoelasticity; Maxwell models; Fractional calculus; Rheology and fluid dynamics;

 

[Back]

 

==========================================================================

The End of This Issue

∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽