FDA Express Vol. 43, No. 3, Jun. 30, 2022
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.cn, fda@hhu.edu.cn
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◆ Latest SCI Journal Papers on FDA
◆ 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
◆ Websites of Interest Fractal Derivative and Operators and Their Applications Fractional Calculus & Applied Analysis ======================================================================== Latest SCI Journal Papers on FDA ------------------------------------------
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
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
By: Sadiya, U; Inc, M; etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 16 Page: 594-607 Published: Dec 31 2022
By:Subramanian, M; Manigandan, M; etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume:16 Page:1-23 Published: Dec 31 2022
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
By:Zhou, WH; Li, HL and Zhang, ZW
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 200 Page:128-147 Published: Oct 2022
By:Omran, AK; Zaky, MA; etc.
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 200 Page:218-239 Published:Oct 2022
By: Saadeh, R; Burqan, A and El-Ajou, A
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page: 10551-10562 Published: Dec 2022
By:Qiyas, M; Naeem, M; etc.
ALEXANDRIA ENGINEERING JOURNAL Volume: 61 Page:10433-10452 Published: Dec 2022
By:Wang, ZB; Ou, CX and Vong, S
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 414 Published: Nov 2022
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
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
========================================================================== Call for Papers ------------------------------------------
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.
=========================================================================== Books ------------------------------------------ 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
======================================================================== Journals ------------------------------------------ Communications in Nonlinear Science and Numerical Simulation (Selected) Somayeh Nemati, Zahra Rezaei Kalansara A. Soltani Joujehi, M. H. Derakhshan, H. R. Marasi M. M. Alsuyuti, E. H. Doha, S. S. Ezz-Eldien Alireza Ansari, Mohammad Hossein Derakhshan, Hassan Askari Sachin Bhalekar, Prashant M. Gade Wenyuan Li, Anatoly Alikhanov, Yalchin Efendiev, Wing Tat Leung N. Padmaja, P. Balasubramaniam G.Narayanan, M.Syed Ali, Hamed Alsulami, Bashir Ahmad, J.J. Trujillo Huilin Lv, Shenzhou Zheng Nguyen Phuong Dong, Hoang Viet Long, Nguyen Thi Kim Son P. Prakash, K. S. Priyendhu, M. Lakshmanan Eric Ngondiep S. Banihashemi, H. Jafari, A. Babaei Hengfei Ding, Qian Yi Fan Kong, Huimin Zhang, Yixin Zhang, Panpan Chao, Wei He Fractional Calculus and Applied Analysis (Volume 25, issue 2) Stéphane Victor, Kendric Ruiz, Pierre Melchior, Serge Chaumette Nikolai Leonenko, Igor Podlubny Ivo Petráš Jia Wei He, Yong Zhou Xiao-Li Ding, Juan J. Nieto, Xiaolong Wang Yingjie Liang, Yue Yu, Richard L. Magin Christian Bender, Yana A. Butko Giovanni E. Comi, Daniel Spector, Giorgio Stefani Luisa Beghin, Alessandro De Gregorio Hassan Emamirad, Arnaud Rougirel Le Chen, Guannan Hu F. M. Atıcı, J. M. Jonnalagadda Guo-Cheng Wu, Hua Kong, Maokang Luo, Hui Fu & Lan-Lan Huang Vladyslav Litovchenko M. Younus Bhat, Aamir H. Dar Thai Son Doan, Peter E. Kloeden Richard Paris Binjie Li, Hao Luo, Xiaoping Xie Mounir Zili, Eya Zougar Shibendu Mahata, Norbert Herencsar, Baris Baykant Alagoz & Celaleddin Yeroglu Sekhar Ghosh, Dumitru Motreanu ======================================================================== Paper Highlight A discussion on nonlocality: From fractional derivative model to peridynamic model HongGuang Sun, Yuanyuan Wang, Lin Yu,Xiangnan Yu
A low-cost computational method for solving nonlinear fractional delay differential equations
Galerkin operational approach for multi-dimensions fractional differential equations
Stability analysis of fixed point of fractional-order coupled map lattices
Partially explicit time discretization for nonlinear time fractional diffusion equations
Dynamical repulsive fractional potential fields in 3D environment
Monte Carlo method for fractional-order differentiation
The fractional-order Lorenz-type systems: A review
Hölder regularity for non-autonomous fractional evolution equations
Stochastic solutions of generalized time-fractional evolution equations
The fractional variation and the precise representative of BVα,p functions
Delsarte equation for Caputo operator of fractional calculus
Hölder regularity for the nonlinear stochastic time-fractional slow & fast diffusion equations on Rd
An eigenvalue problem in fractional h-discrete calculus
The Cauchy problem and distribution of local fluctuations of one Riesz gravitational field
Fractional vector-valued nonuniform MRA and associated wavelet packets on L2(R,CM)
Attractors of Caputo fractional differential equations with triangular vector fields
Asymptotics of the Mittag-Leffler function Ea(z) on the negative real axis when a→1
Mixed stochastic heat equation with fractional Laplacian and gradient perturbation
Optimal F-domain stabilization technique for reduction of commensurate fractional-order SISO systems
Infinitely many large solutions to a variable order nonlocal singular equation
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 ------------------------------------- Hui Zhang, Fanhai Zeng, Xiaoyun Jiang & George Em Karniadakis Publication information: Fractional Calculus and Applied Analysis: Published: 03 May 2022 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 ========================================================================== The End of This Issue ∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽
Convergence analysis of the time-stepping numerical methods for time-fractional nonlinear subdiffusion equations
https://doi.org/10.1007/s13540-022-00022-6