FDA Express Vol. 43, No. 3, Jun. 30, 2022

发布时间:2022-06-30 访问量:1800

FDA Express    Vol. 43, No. 3, Jun. 30, 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.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 43_No 3_2022.pdf


 

◆  Latest SCI Journal Papers on FDA

(Searched on Jun. 30, 2022)

 

  Call for Papers

Novel Numerical Solutions of Fractional PDEs

ICFCAM 2022: 16. International Conference on Fractional Calculus and Applied Mathematics


 

◆  Books

Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

 

◆  Journals

Communications in Nonlinear Science and Numerical Simulation

Fractional Calculus and Applied Analysis

 

  Paper Highlight

A discussion on nonlocality: From fractional derivative model to peridynamic model

Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations

 

  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 Jun. 30, 2022)



 Fractional diffusion model for emission and adsorption prediction of TXIB from wallpaper

By: Zhang, Yan; Liu, Mengqi; etc.
Environmental science and pollution research international Published: 2022-Jun-23


 A New Look at the Initial Condition Problem

By:Ortigueira, MD
MATHEMATICS Volume: 10 Published: ‏May 2022



 On the Equivalence between Integer- and Fractional Order-Models of Continuous-Time and Discrete-Time ARMA Systems

By: Ortigueira, MD and Magin, RL
FRACTAL AND FRACTIONAL Volume:6    Published: ‏ May 2022



 The 21st Century Systems: An Updated Vision of Continuous-Time Fractional Models

By:Ortigueira, MD and Machado, JT
IEEE CIRCUITS AND SYSTEMS MAGAZINE Volume: ‏22 Page:36-56 Published: 2022



 How Many Fractional Derivatives Are There?

By: Duarte Valério; Manuel D. Ortigueira; etc.
Mathematics Volume: ‏ 10 Published: 2022



 Consistent travelling waves solutions to the non-linear time fractional Klein-Gordon and Sine-Gordon equations through extended tanh-function approach

By: Sadiya, U; Inc, M; etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: ‏16 Page: 594-607 Published: ‏ Dec 31 2022



 On system of nonlinear coupled differential equations and inclusions involving Caputo-type sequential derivatives of fractional order

By:Subramanian, M; Manigandan, M; etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume:16 Page:1-23 Published: Dec 31 2022



 Dynamical behaviours and soliton solutions of the conformable fractional Schrodinger-Hirota equation using two different methods

By:Koprulu, MO
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: ‏ 16 Page:66-74 Published: ‏ Dec 31 2022



 Two approximation methods for fractional order Pseudo-Parabolic differential equations

By: Modanli, M; Goktepe, E; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page:10333-10339 Published: Dec 2022



 A novel seasonal fractional grey model for predicting electricity demand: A case study of Zhejiang in China

By:Zhou, WH; Li, HL and Zhang, ZW
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 200 Page:128-147 Published: Oct 2022



 An easy to implement linearized numerical scheme for fractional reaction-diffusion equations with a prehistorical nonlinear source function

By:Omran, AK; Zaky, MA; etc.
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 200 Page:218-239 Published:Oct 2022



 Reliable solutions to fractional Lane-Emden equations via Laplace transform and residual error function

By: Saadeh, R; Burqan, A and El-Ajou, A
ALEXANDRIA ENGINEERING JOURNAL Volume: ‏ 61 Page: 10551-10562 Published: ‏ Dec 2022



 Fractional orthotriple fuzzy rough Hamacher aggregation operators and-their application on service quality of wireless network selection

By:Qiyas, M; Naeem, M; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: ‏ 61 Page:10433-10452 Published: ‏ Dec 2022



 A second-order scheme with nonuniform time grids for Caputo-Hadamard fractional sub-diffusion equations?

By:Wang, ZB; Ou, CX and Vong, S
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 414 Published: Nov 2022



 Error analysis of spectral approximation for space-time fractional optimal control problems with control and state constraints

By: Chen, YP; Lin, XX and Huang, YQ
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: ‏ 413 Published: ‏ Oct 15 2022



 Restrictions on parameters in distributed order fractional linear constitutive equations

By: Atanackovi, TM; Janev, M and Pilipovi, S
APPLIED MATHEMATICAL MODELLING Volume: ‏110 Page:99-111 Published: ‏ Oct 2022



 Algebraic estimation for fractional integrals of noisy acceleration based on the behaviour of fractional derivatives at zero

By:Wang, ZB; Liu, DY and Boutat, D
APPLIED MATHEMATICS AND COMPUTATION Volume: 430 Published:Oct 1 2022 |



 Fast difference scheme for a tempered fractional Burgers equation in porous media

By:Wang, HH and Li, C
APPLIED MATHEMATICS LETTERS Volume: ‏ 132 Published: Oct 2022



 Lie symmetries reduction and spectral methods on the fractional two-dimensional heat equation

By:Bakhshandeh-Chamazkoti, R and Alipour, M
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 200 Published: Oct 2022


 

 

 

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Call for Papers

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Novel Numerical Solutions of Fractional PDEs

( A special issue of Fractal and Fractional )


Dear Colleagues: During the past few decades, fractional partial differential equations (PDEs) have been widely used in biology, materials science, molecular dynamics and many other fields. In particular, time fractional PDEs, which are able to accurately describe the state or evolution with historical memory, have attracted much research interest in both theoretical and numerical aspects. Due to the non-local property of fractional derivatives, the development of numerical algorithms for the fractional PDEs faces new challenges and opportunities:

(1) Analysis and numerical treatment of the weak singularity of solutions;
(2) Fast and parallel algorithms;
(3) Applications and simulations for real-word models.


Keywords:

- Fractional PDE
- Fractional ODE
- Integro-differential equation
- Numerical method
- Fast algorithm
- Modeling and simulation



Organizers:

Prof. Dr. Xiaoping Xie
Dr. Xian-Ming Gu
Dr. Maohua Ran
Guest Editors

Important Dates:

Deadline for manuscript submissions: 31 July 2022.

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



ICFCAM 2022: 16. International Conference on Fractional Calculus and Applied Mathematics

( August 16-17, 2022 in Venice, Italy )


Dear Colleagues: International Conference on Fractional Calculus and Applied Mathematics 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 and Applied Mathematics. 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 and Applied Mathematics.

Prospective authors are kindly encouraged to contribute to and help shape the conference through submissions of their research abstracts, papers and e-posters. Also, high quality research contributions describing original and unpublished results of conceptual, constructive, empirical, experimental, or theoretical work in all areas of Fractional Calculus and Applied Mathematics are cordially invited for presentation at the conference. The conference solicits contributions of abstracts, papers and e-posters that address themes and topics of the conference, including figures, tables and references of novel research materials.


Keywords:

- Applied mathematics - Mathematical methods in continuum mechanics
- Fractional calculus and its applications
- Optimization and control in engineering
- Mathematical modelling with engineering applications
- Non-Linear dynamical systems and chaos
- Scientific computing and algorithms
- Stochastic differential equations
- Linear algebra and applications
- Combinatorial linear algebra
- Numerical linear analysis



Important Dates:

Deadline for manuscript submissions: June 30, 2022.

All details on this conference are now available at: https://waset.org/fractional-calculus-and-applied-mathematics-conference-in-august-2022-in-venice.





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Books

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Fractional Dynamic Calculus and Fractional Dynamic Equations on Time Scales

( Authors: Svetlin G. Georgiev )

Details:https://doi.org/10.1007/978-3-319-73954-0

Book Description:

Pedagogically organized, this monograph introduces fractional calculus and fractional dynamic equations on time scales in relation to mathematical physics applications and problems. Beginning with the definitions of forward and backward jump operators, the book builds from Stefan Hilger’s basic theories on time scales and examines recent developments within the field of fractional calculus and fractional equations. Useful tools are provided for solving differential and integral equations as well as various problems involving special functions of mathematical physics and their extensions and generalizations in one and more variables. Much discussion is devoted to Riemann-Liouville fractional dynamic equations and Caputo fractional dynamic equations. Intended for use in the field and designed for students without an extensive mathematical background, this book is suitable for graduate courses and researchers looking for an introduction to fractional dynamic calculus and equations on time scales.


Author Biography:

Svetlin Georgiev is in the Department of Differential Equations of the Faculty of Mathematics and Informatics at Sofia University, Bulgaria.

Contents:

Front Matter

Elements of Time Scale Calculus
Abstract; Forward and Backward Jump Operators, Graininess Function; Differentiation; Mean Value Theorems; Integration; The Exponential Function; Hyperbolic and Trigonometric Functions; Dynamic Equations; Power Series on Time Scales; Advanced Practical Problems; References;

The Laplace Transform on Time Scales
Abstract; Definition and Properties; The Laplace Transform on Isolated Time Scales; Advanced Practical Problems;

Convolution on Time Scales
Abstract; Shifts and Convolutions; Convolutions; The Convolution Theorem; Advanced Practical Problems;

The Riemann–Liouville Fractional Δ-Integral and the Riemann–Liouville Fractional Δ-Derivative on Time Scales
Abstract; The Δ-Power Function; Definition of the Riemann–Liouville Fractional Δ-Integral and the Riemann–Liouville Fractional Δ-Derivative; Properties of the Riemann–Liouville Fractional Δ-Integral and the Riemann–Liouville Fractional Δ-Derivative on Time Scales; Advanced Practical Problems;

Cauchy-Type Problems with the Riemann–Liouville Fractional Δ-Derivative
Abstract; Existence and Uniqueness of Solutions; The Dependence of the Solution on the Initial Data;

Riemann–Liouville Fractional Dynamic Equations with Constant Coefficients
Abstract; Homogeneous Riemann–Liouville Fractional Dynamic Equations with Constant Coefficients; Inhomogeneous Riemann–Liouville Fractional Dynamic Equations with Constant Coefficients; Advanced Practical Problems;

The Caputo Fractional Δ-Derivative on Time Scales
Abstract; Definition of the Caputo Fractional Δ-Derivative and Examples; Properties of the Caputo Fractional Δ-Derivative; Advanced Practical Problems;

Cauchy-Type Problems with the Caputo Fractional Δ-Derivative
Abstract; Existence and Uniqueness of the Solution to the Cauchy-Type Problem; The Dependence of the Solution on the Initial Value;

Caputo Fractional Dynamic Equations with Constant Coefficients
Abstract; Homogeneous Caputo Fractional Dynamic Equations with Constant Coefficients; Inhomogeneous Caputo Fractional Dynamic Equations with Constant Coefficients; Advanced Practical Problems;

Appendix: The Gamma Function
Abstract; Definition of the Gamma Function; Some Properties of the Gamma Function; Limit Representation of the Gamma Function;

Appendix: The Beta Function
Abstract; Definition of the Beta Function; Properties of the Beta Function; An Application;

Back Matter



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 Journals

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Communications in Nonlinear Science and Numerical Simulation

 (Selected)

 


 A low-cost computational method for solving nonlinear fractional delay differential equations

Somayeh Nemati, Zahra Rezaei Kalansara


 An efficient hybrid numerical method for multi-term time fractional partial differential equations in fluid mechanics with convergence and error analysis

A. Soltani Joujehi, M. H. Derakhshan, H. R. Marasi


 Galerkin operational approach for multi-dimensions fractional differential equations

M. M. Alsuyuti, E. H. Doha, S. S. Ezz-Eldien


 Distributed order fractional diffusion equation with fractional Laplacian in axisymmetric cylindrical configuration

Alireza Ansari, Mohammad Hossein Derakhshan, Hassan Askari


 Stability analysis of fixed point of fractional-order coupled map lattices

Sachin Bhalekar, Prashant M. Gade


 Partially explicit time discretization for nonlinear time fractional diffusion equations

Wenyuan Li, Anatoly Alikhanov, Yalchin Efendiev, Wing Tat Leung


 Design of H/passive state feedback control for delayed fractional order gene regulatory networks via new improved integral inequalities

N. Padmaja, P. Balasubramaniam


 A hybrid impulsive and sampled-data control for fractional-order delayed reaction–diffusion system of mRNA and protein in regulatory mechanisms

G.Narayanan, M.Syed Ali, Hamed Alsulami, Bashir Ahmad, J.J. Trujillo


 Ground states for Schrödinger–Kirchhoff equations of fractional p-Laplacian involving logarithmic and critical nonlinearity

Huilin Lv, Shenzhou Zheng


 The dynamical behaviors of fractional-order SE1E2IQR epidemic model for malware propagation on Wireless Sensor Network

Nguyen Phuong Dong, Hoang Viet Long, Nguyen Thi Kim Son


 Invariant subspace method for (m+1)-dimensional non-linear time-fractional partial differential equations

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


 A two-level fourth-order approach for time-fractional convection–diffusion–reaction equation with variable coefficients

Eric Ngondiep


 An efficient computational scheme to solve a class of fractional stochastic systems with mixed delays

S. Banihashemi, H. Jafari, A. Babaei


 The construction of higher-order numerical approximation formula for Riesz derivative and its application to nonlinear fractional differential equations (I)

Hengfei Ding, Qian Yi


 Stationary response determination of MDOF fractional nonlinear systems subjected to combined colored noise and periodic excitation

Fan Kong, Huimin Zhang, Yixin Zhang, Panpan Chao, Wei He

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Fractional Calculus and Applied Analysis

  (Volume 25, issue 2)

 


  Dynamical repulsive fractional potential fields in 3D environment

Stéphane Victor, Kendric Ruiz, Pierre Melchior, Serge Chaumette


 Monte Carlo method for fractional-order differentiation

Nikolai Leonenko, Igor Podlubny


 The fractional-order Lorenz-type systems: A review

Ivo Petráš


 Hölder regularity for non-autonomous fractional evolution equations

Jia Wei He, Yong Zhou


 Analytical solutions for fractional partial delay differential-algebraic equations with Dirichlet boundary conditions defined on a finite domain

Xiao-Li Ding, Juan J. Nieto, Xiaolong Wang


 Computation of the inverse Mittag–Leffler function and its application to modeling ultraslow dynamics

Yingjie Liang, Yue Yu, Richard L. Magin


 Stochastic solutions of generalized time-fractional evolution equations

Christian Bender, Yana A. Butko


 The fractional variation and the precise representative of BVα,p functions

Giovanni E. Comi, Daniel Spector, Giorgio Stefani


 On mild solutions of the generalized nonlinear fractional pseudo-parabolic equation with a nonlocal condition

Luisa Beghin, Alessandro De Gregorio


 Delsarte equation for Caputo operator of fractional calculus

Hassan Emamirad, Arnaud Rougirel


 Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on Rd

Le Chen, Guannan Hu


 An eigenvalue problem in fractional h-discrete calculus

F. M. Atıcı, J. M. Jonnalagadda


 Unified predictor–corrector method for fractional differential equations with general kernel functions

Guo-Cheng Wu, Hua Kong, Maokang Luo, Hui Fu & Lan-Lan Huang


 The Cauchy problem and distribution of local fluctuations of one Riesz gravitational field

Vladyslav Litovchenko


 Fractional vector-valued nonuniform MRA and associated wavelet packets on L2(R,CM)

M. Younus Bhat, Aamir H. Dar


 Attractors of Caputo fractional differential equations with triangular vector fields

Thai Son Doan, Peter E. Kloeden


 Asymptotics of the Mittag-Leffler function Ea(z) on the negative real axis when a→1

Richard Paris


 Error estimation of a discontinuous Galerkin method for time fractional subdiffusion problems with nonsmooth data

Binjie Li, Hao Luo, Xiaoping Xie


 Mixed stochastic heat equation with fractional Laplacian and gradient perturbation

Mounir Zili, Eya Zougar


 Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems

Shibendu Mahata, Norbert Herencsar, Baris Baykant Alagoz & Celaleddin Yeroglu


 Infinitely many large solutions to a variable order nonlocal singular equation

Sekhar Ghosh, Dumitru Motreanu

 

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 Paper Highlight

A discussion on nonlocality: From fractional derivative model to peridynamic model

HongGuang Sun, Yuanyuan Wang, Lin Yu,Xiangnan Yu  

Publication information: Communications in Nonlinear Science and Numerical Simulation: Published: Volume 114, November 2022

https://doi.org/10.1016/j.cnsns.2022.106604


Abstract

Characterization of nonlocality is an open problem in physics and engineering. This paper conducts a detailed investigation on two nonlocal models, namely, the fractional derivative model and the peridynamic model for anomalous diffusion. A generalized nonlocal model combining the advantages of the fractional derivative model and the peridynamic model, is introduced. In this paper, analytical solutions and the mean squared displacements of the two models are provided and discussed. In addition, their intrinsic relations and notable differences are investigated. Preliminary applications indicate that the peridynamic model can well capture an unremarkable transition from normal-diffusion to super-diffusion, while the fractional derivative model presents super-diffusion behaviors in the whole process. At last, a generalized nonlocal operator is proposed as a more general strategy to solve nonlocal problems.


Keywords

Fractional derivative model; Peridynamic model; Mean squared displacement; Nonlocality; Super-diffusion

 

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Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations

  Hui Zhang, Fanhai Zeng, Xiaoyun Jiang & George Em Karniadakis

Publication information: Fractional Calculus and Applied Analysis: Published: 03 May 2022
https://doi.org/10.1007/s13540-022-00022-6


 

Abstract

In 1986, Dixon and McKee (Z Angew Math Mech 66:535–544, 1986) developed a discrete fractional Gronwall inequality, which can be seen as a generalization of the classical discrete Gronwall inequality. However, this generalized discrete Gronwall inequality and its variant (Al-Maskari and Karaa in SIAM J Numer Anal 57:1524–1544, 2019) have not been widely applied in the numerical analysis of the time-stepping methods for the time-fractional evolution equations. The main purpose of this paper is to show how to apply the generalized discrete Gronwall inequality to prove the convergence of a class of time-stepping numerical methods for time-fractional nonlinear subdiffusion equations, including the popular fractional backward difference type methods of order one and two, and the fractional Crank-Nicolson type methods. We obtain the optimal L2 error estimate in space discretization for multi-dimensional problems. The convergence of the fast time-stepping numerical methods is also proved in a simple manner. The present work unifies the convergence analysis of several existing time-stepping schemes. Numerical examples are provided to verify the effectiveness of the present method.


Keywords

Time-fractional nonlinear subdiffusion equations; Discrete fractional Gronwall inequality; Fast time-stepping methods; Convergence analysis

 

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The End of This Issue

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