FDA Express    Vol. 46, No. 3, Mar. 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.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 46_No 3_2023.pdf

◆  Latest SCI Journal Papers on FDA

(Searched on Mar. 31, 2023)

◆  Call for Papers

The 4th International Symposium on Operational and Stochastic Methods in Fractional Dynamics

Application of Fractional-Calculus in Physical Systems

◆  Books

Numerical Treatment and Analysis of Time-Fractional Evolution Equations

◆  Journals

Communications in Nonlinear Science and Numerical Simulation

Fractional Calculus and Applied Analysis

◆  Paper Highlight

New description of the mechanical creep response of rocks by fractional derivative theory

Modeling immiscible fluid flow in fractal pore medium by multiphase lattice Boltzmann flux solver

◆  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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(Searched on Mar. 31, 2023)

 Event-Triggered Finite-Time Tracking Control for Fractional-Order Multi-Agent Systems with Input Saturation and Constraints

By: Hu, LL and Yu, H
APPLIED ARTIFICIAL INTELLIGENCE Volume: 37 Published: Dec 31 2023

 A comparative study on the applicability and effectiveness of NSVI and NDVI for estimating fractional vegetation cover based on multi-source remote sensing image

By:Xu, ZH; Li, YF; etc.
GEOCARTO INTERNATIONAL Volume: 38 Published: Dec 31 2023

 On the Dirichlet BVP of fractional diffusion advection reaction equation in bounded interval: Structure of solution, integral equation and approximation

By:Li, YL and Ginting, V
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 426 Published: Jul 2023

 A level set based fractional order variational model for motion estimation in application oriented spectrum

By:Khan, M and Kumar, P
EXPERT SYSTEMS WITH APPLICATIONS Volume: 219 Published: Jun 2023

 Existence and Multiplicity of Solutions for a Fractional Schrodinger-Poisson System with Subcritical or Critical Growth

By: Gu, GZ; Mu, CY and Yang, ZP
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: ‏22 Published: Jun 2023

 Exact Controllability of Hilfer Fractional Differential System with Non-instantaneous Impluleses and State Dependent Delay

By:Khan, A; Ain, QT; etc.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: 22 Published: ‏ Jun 2023

 Rayleigh-Faber-Krahn, Lyapunov and Hartmann-Wintner Inequalities for Fractional Elliptic Problems

By:Kassymov, A; Ruzhansky, M and Torebek, BT
MEDITERRANEAN JOURNAL OF MATHEMATICS Volume:20 Published:Jun 2023

 Existence and Stability Results for Impulsive Implicit Fractional Differential Equations with Delay and Riesz-Caputo Derivative

By:Rahou, W; Salim, A; etc.
MEDITERRANEAN JOURNAL OF MATHEMATICS Volume:20 Published: Jun 2023

 On Existence and Continuity Results of Solution for Multi-time Scale Fractional Stochastic Differential Equation

By: Alkhazzan, A; Wang, JG; etc.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: 22 Published: Jun 2023

 Solution of space-time tempered fractional diffusion-wave equation using a high-order numerical method

By:Saffarian, M and Mohebbi, A
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 423 Published: May 15 2023

 Fractional p-Laplacian Problem with Critical Stein-Weiss Type Term

By:Su, Y
JOURNAL OF GEOMETRIC ANALYSIS Volume: 33 Published: May 2023

 Normalized Solutions of Mass Subcritical Fractional Schrodinger Equations in Exterior Domains

By: Yu, SB; Tang, CL and Zhang, ZH
JOURNAL OF GEOMETRIC ANALYSIS Volume: 33 Published: May 2023

 Numerical simulation of the fractional diffusion equation

By:Partohaghighi, M; Yusuf, A; etc.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B Volume:37 Published: Apr 20 2023

 Solving fuzzy fractional differential equations with applications

By:Osman, M and Xia, YH
ALEXANDRIA ENGINEERING JOURNAL Volume:69 Page:529-559 Published: Apr 15 2023 |

 Comparison of vessel fractional flow reserve with invasive resting full-cycle ratio in patients with intermediate coronary lesions

By: Lake, Philipp; Halbach, Marcel; etc.
INTERNATIONAL JOURNAL OF CARDIOLOGY Volume:377 Page:1-8 Published: 2023-apr-15

 Unconditionally convergent and superconvergent FEMs for nonlinear coupled time-fractional prey-predator problem

By:Lu, Y and Li, M
COMPUTERS & MATHEMATICS WITH APPLICATIONS Volume:42 Published: Apr 2023

 Sparse optimization problems in fractional order Sobolev spaces

By:Antil, H and Wachsmuth, D
INVERSE PROBLEMS Volume: 39 Published:Apr 1 2023 |

 A variety of solitary waves solutions for the modified nonlinear Schrodinger equation with conformable fractional derivative

By:Sadaf, M; Arshed, S and Akram, G
OPTICAL AND QUANTUM ELECTRONICS Volume: 55 Published: Apr 2023

 Numerical solutions of fractional epidemic models with generalized Caputo-type derivatives

By:Hajaj, R and Odibat, Z
PHYSICA SCRIPTA Volume: 98 Published: Apr 1 2023

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Call for Papers

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The 4th International Symposium on Operational and Stochastic Methods in Fractional Dynamics

( September 5-9, 2023 in Kraków, Poland)

Dear Colleagues: The goal of the conference is to give researchers working in the field of fractional dynamics an opportunity to meet “in person’ and to discuss problems whose investigation requires methods of fractional dynamics. We revive the tradition, unfortunately interrupted by the Covid19 pandemic, of conferences devoted to the subject and held in Kraków in 2016 and 2018. The leading topic of is to present and discuss recent results obtained in the investigations of phenomena that take place in complex systems and are governed by memory-dependent time evolution equations. The scientific program of the conference will be focused on theoretical studies of anomalous diffusion and the non-Debye dielectric relaxation but we are not going to restrict discussed subjects solely to these problems. The interdisciplinary nature of fractional dynamics causes that we are also deeply interested in pushing forward the development of mathematical tools used within it, in particular those which merge operational calculus with probabilistic and stochastic methods.

We believe that the conference, expected and believed to be free and unhindered exchange of new ideas, will be an incipience of new collaborations and common research projects rooted not only in sharing scientific interests but also in the intimate nature of our conference, its friendly atmosphere and genius loci of Kraków.

Keywords:

- Fractional differential equations
- Fractional integral equations
- Fractional integro-differential equations
- Anomalous diffusion
- Non-Debye dielectric relaxation

Organizers:

Katarzyna Górska
Andrzej Horzela
Tobiasz Pietrzak
Guest Editors

Important Dates:

Deadline for conference receipts: June 15, 2023

All details on this conference are now available at: https://indico.ifj.edu.pl/event/878.

Application of Fractional-Calculus in Physical Systems

( A special issue of Fractal and Fractional )

Dear Colleagues: It is well known that fractional calculus has numerous applications in engineering, science, and technology. The dynamics of challenging physical systems are closely connected to fractional calculus. Due to their non-local nature, fractional operators can more accurately and systematically represent a variety of natural phenomena. Fractional order differential equations may correctly control a wide variety of mathematical and physical models. It follows that the conclusions for the fractional mathematical model are more accurate and broader since the classical models are specific examples of the fractional order mathematical models. Fractional calculus also offers a number of techniques for resolving nonlinear models, integro-differential equations, and differential, integral, and integral-differential equations in mathematical physics. Fractional calculus on the complex plane has received a lot of attention in the last 10 years. The connection between fractional calculus and other mathematical and physical disciplines may open up new study directions and lead to new discoveries and applications. The purpose of this Special Issue is to bring together top academicians and researchers from a variety of engineering disciplines including applied mathematicians and physics, moreover, to provide them a forum to present their creative research. The fundamental focus of the articles includes theoretical, analytical, and numerical approaches with cutting-edge mathematical modeling and new advancements in differential and integral equations of arbitrary order originating in physical systems. Fractional calculus and its application for physical systems is a topic of extensive theoretical and analytical research around the world. Recent contributions to this essentially interdisciplinary field from theoretical, analytical, numerical, and computational perspectives are the focus of this Special Issue. This Special Issue collects original research work on recent developments in fractional calculus including:

- Fractional calculus in physical systems;
- Fractional differential equations;
- Modeling and simulation;
- Fractional dynamical system;
- Fractional control theory;
- Numerical methods;
- Fractional calculus and chaos;
- Non-locality and memory effects;
- Non-locality in physical systems;
- Modeling biological phenomena;
- Non-locality in epidemic models;
- Theoretical and computational analysis.

Keywords:

- Fractional-calculus
- Physical systems
- Mathematical modeling
- Theoretical and computational analysis
- Epidemic models
- Numerical analysis

Organizers:

Prof. Dr. Salah Mahmoud Boulaaras
Dr. Viet-Thanh Pham
Dr. Rashid Jan
Guest Editors

Important Dates:

Deadline for manuscript submissions: 10 April 2023.

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

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Books

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Numerical Treatment and Analysis of Time-Fractional Evolution Equations

( Authors: Bangti Jin , Zhi Zhou )

Details:https://doi.org/10.1007/978-3-031-21050-1

Book Description:

This book discusses numerical methods for solving time-fractional evolution equations. The approach is based on first discretizing in the spatial variables by the Galerkin finite element method, using piecewise linear trial functions, and then applying suitable time stepping schemes, of the type either convolution quadrature or finite difference. The main concern is on stability and error analysis of approximate solutions, efficient implementation and qualitative properties, under various regularity assumptions on the problem data, using tools from semigroup theory and Laplace transform. The book provides a comprehensive survey on the present ideas and methods of analysis, and it covers most important topics in this active area of research. It is recommended for graduate students and researchers in applied and computational mathematics, particularly numerical analysis.

Author Biography:

Bangti JinView, Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong
Zhi Zhou, Department of Applied Mathematics, Hong Kong Polytechnic University, Hung hom, Hong Kong

Contents:

Front Matter

Existence, Uniqueness, and Regularity of Solutions
Abstract; Basics of Fractional Calculus; Mittag–Leffler Function; Existence, Uniqueness, and Sobolev Regularity; Notes;

Spatially Semidiscrete Discretization
Abstract; Galerkin Finite Element Method; Error Analysis via Mittag–Leffler Functions; Error Analysis via Laplace Transform; Lumped Mass FEM;

Convolution Quadrature
Abstract; Convolution Quadrature Generated by BDF; BDFk CQ with Initial Correction; Fractional Crank–Nicolson Scheme; Parallel in Time Algorithm; Fast Convolution; Notes;

Finite Difference Methods: Construction and Implementation
Abstract; Construction of Time-Stepping Schemes; Sum of Exponential Approximation; Notes;

Finite Difference Methods on Uniform Meshes
Abstract; Error Analysis of L1 Scheme; Corrected L1 Scheme;

Finite Difference Methods on Graded Meshes
Abstract; Error Analysis via Nonuniform Gronwall’s Inequality; Error Analysis of the L1 Scheme via Barrier Functions; Error Analysis of Alikhanov’s Scheme via Barrier Functions;

Nonnegativity Preservation
Abstract; Nonnegativity Preservation; Spatially Semidiscrete Methods; Fully Discrete Scheme; Maximum-Norm Contractivity;

Discrete Maximal Regularity
Abstract; R-Boundedness, UMD Spaces, and Fourier Multiplier Theorems; Convolution Quadrature Generated by BDF; L1 Scheme; Explicit Euler Method; Fractional Crank–Nicolson Method; Inhomogeneous Initial Condition;

Subdiffusion with Time-Dependent Coefficients
Abstract; Regularity Theory; Semidiscrete Galerkin FEM; Time Discretization by Backward Euler CQ; Time Discretization by Corrected BDF2 CQ;

Semilinear Subdiffusion
Abstract; Discrete Gronwall’s Inequality; Error Estimates for the Linearized Scheme; High-Order Time-Stepping Schemes;

Time-Space Finite Element Approximation
Abstract; Time-Space Petrov–Galerkin Formulation; Petrov–Galerkin FEM on Tensor-Product Meshes; Error Estimates;

Spectral Galerkin Approximation
Abstract; Time-Space Galerkin Formulation; Log Orthogonal Functions; Spectral Galerkin Method; Fully Discrete Scheme; Fast Linear Solver;

Incomplete Iterative Solution at Time Levels
Abstract; Incomplete Iterative Scheme; Error Analysis for Smooth Initial Data; Error Analysis for Nonsmooth Initial Data;

Optimal Control with Subdiffusion Constraint
Abstract; Regularity Theory; Numerical Approximation of the Forward Problem; Numerical Approximation of the Optimal Control Problem;

Backward Subdiffusion

Back Matter

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 Journals

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Communications in Nonlinear Science and Numerical Simulation

 (Selected)

 Probabilistic evolution analysis and first passage analysis of a class of stochastic dynamic systems with fractional derivative based on Complex Fractional Moment method

Lizhi Niu, Wei Xu, etc.

 Fractional derivative truncation approximation for real-time applications

Jean-François Duhé, Stéphane Victor, etc.

 Fractional-order modeling and optimal control of a new online game addiction model based on real data

Youming Guo, Tingting Li

 Invariant subspace method to the initial and boundary value problem of the higher dimensional nonlinear time-fractional PDEs

K. S. Priyendhu, P. Prakash, M. Lakshmanan

 A fractional optimal control model for a simple cash balance problem

Yi Chen, Zhanmei Lv

 A survey on random fractional differential equations involving the generalized Caputo fractional-order derivative

Ho Vu, Nguyen Dinh Phu, Ngo Van Hoa

 A split-step Fourier pseudo-spectral method for solving the space fractional coupled nonlinear Schrödinger equations

F. Abdolabadi, A. Zakeri, A. Amiraslani

 Complex-order fractional diffusion in reaction-diffusion systems

Alfonso Bueno-Orovio, Kevin Burrage

 Bifurcations analysis of a multiple attractors energy harvesting system with fractional derivative damping under random excitation

Wenting Zhang, Wei Xu, etc.

 Finiteness conditions for performance indices in generalized fractional-order systems defined based on the regularized Prabhakar derivative

Shiva Eshaghi, Mohammad Saleh Tavazoei

 On the equivalence between fractional and classical oscillators

Paweł Łabędzki, Rafał Pawlikowski

 Ritz-generalized Pell wavelet method: Application for two classes of fractional pantograph problems

Sedigheh Sabermahani, Yadollah Ordokhani, etc.

 Two methods for studying the response and the reliability of a fractional stochastic dynamical system

Wei Li, Yu Guan, etc.

 Fractional damping effects on the transient dynamics of the Duffing oscillator

Mattia Coccolo, Jesús M. Seoane, etc.

 On the existence of traveling fronts in the fractional-order Amari neural field model

L. R. González-Ramírez

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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

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 Paper Highlight

New description of the mechanical creep response of rocks by fractional derivative theory

Toungainbo Cédric Kamdem, Kol Guy Richard, Tibi Béda  

Publication information: Applied Mathematical Modelling Volume 116, April 2023.

https://doi.org/10.1016/j.apm.2022.11.036

Abstract

Accurate estimation and modeling of rock behavior during creep is an essential step to ensure reliability safety in the engineering of underground structures. In this work we proposed a new way of adjusting the fractional order to obtain a new variable fractional order rheological model to describe the evolution of mechanical properties and to model the full- creep response. It is proved that the function law of our variable order fractional model is defined only by four parameters . An analysis on the different parameters of the fractional model shows that the mechanical behavior of the rock softens faster when the temperature and the applied stress level are high and hardens in the opposite case. Moreover, through its derived version, the physical meaning of our fractional model is explored in more detail, as it allows to highlight the hardening/softening duality of the rock behavior. This fractional model allows us to model the full creep behavior of the rock with a reduced number of parameters, a simple form, a sufficiently guaranteed accuracy and a unified law. We believe that the results of this work will be able to help in the decision making during the realization of underground structures.

Key Points

Creep; Fractional order; Mechanical property; Rock

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Modeling immiscible fluid flow in fractal pore medium by multiphase lattice Boltzmann flux solver

  LiJuan Jiang , HongGuang Sun , Yan Wang

Publication information: Physics of Fluids 35, 023334 (2023).
https://doi.org/10.1063/5.0137360

Abstract

In this paper, the multiphase lattice Boltzmann flux solver (MLBFS), where the phase field model and the apparent liquid permeability model are built-in, is developed to simulate incompressible multiphase flows in fractal pore structure at the representative elementary volume scale. MLBFS takes advantage of the traditional Navier–Stokes solver (e.g., geometric flexibility and direct handling of complex boundary conditions) and lattice Boltzmann method (e.g., intrinsically kinetic nature, simplicity, and parallelism). It is easily applied to simulate multiphase flows transport in the porous medium with large density ratios and high Reynolds numbers. This study focuses on the fluid flow in fractal pore structures and provides an in-depth discussion of the effects of non-Newtonian index, fractal parameters, and density ratios on multiphase flow. The proposed model is validated with benchmark problems to test the applicability and reliability of the MLBFS in describing fluid flow in fractal pore structures with large density ratios and viscosity ratios. Simulation results show that the fractal parameters (i.e., fractal dimension, tortuous fractal dimension, porosity, and capillary radius ratio) can accurately characterize fractal pore structure and significantly affect the apparent liquid permeability. In addition, the flow rate increases with the fractal dimension and decreases with the tortuous fractal dimension, while both flow rate and apparent liquid permeability decrease as the capillary radius ratio. It is also noteworthy that the effect of nonlinear drag forces cannot be neglected for shear-thickened flows.

Keywords

Multiphase lattice Boltzmann flux solver; Fractal pore structure; Permeability; Fractional order index; Fractal dimension

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