FDA Express Vol. 37, No. 2, Nov 30, 2020
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Institute of Soft Matter Mechanics, Hohai
University
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◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Fractional Calculus in Magnetic Resonance
◆ Books
Fractional Differential Equations: Finite Difference Methods
◆ Journals
Fractional Calculus and Applied Analysis
◆ Paper Highlight
Towards a unified approach to nonlocal elasticity via fractional-order mechanics
◆ 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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By: Mahor, Teekam Chand; Mishra, Rajshree; Jain, Renu
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 385 Published: MAR 15 2021
Spectral Galerkin schemes for a class of multi-order fractional pantograph equations
Numerical analysis of fractional Volterra integral equations via Bernstein approximation method
Memory-dependent derivative versus fractional derivative (I): Difference in temporal modeling
Discrete fractional calculus for interval-valued systems
A meshless method for time fractional nonlinear mixed diffusion and diffusion-wave equation
Propagation of Gaussian beam based on two-dimensional fractional Schrodinger equation
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Call for Papers
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Fractional Calculus in Magnetic Resonance
(special issue in Mathematics)
The applications of fractional calculus in the field of magnetic resonance are widespread and growing. In particular, fractional calculus can extend the capabilities of nuclear magnetic resonance (NMR), electron spin reso- nance (ESR), and magnetic resonance imaging (MRI) by the generalizing the integer-order derivatives found in the Bloch and Bloch–Torrey equa- tions. Solutions obtained using fractional calculus illuminate the structure and dynamics of materials at the molecular, cellular, and tissue length scales.
In these situations, the space and time-fractional derivatives encode fea- tures that are not completely resolved using standard methods. As a con- sequence, molecular couplings, cell membrane permeability, and imaging biomarkers, for example, can be computed and displayed. These new tech- niques combine the specificity of fractional calculus with the non-perturbing sensitivity of magnetic resonance. The development of these methods and models requires cooperation between experts in magnetic resonance and applied mathematics; cooperation exhibited by the technical, review, and tutorial papers in this Special Issue.
The purpose of this Special Issue is to gather articles reflecting the latest developments of fractional calculus in the fields of nuclear mag- netic resonance (NMR), electron spin resonance (ESR), and magnetic res- onance imaging (MRI). Applications employing fractional calculus in the sub-disciplines of NMR/ESR spectroscopy, relaxation, diffusion, and elas- tography are encouraged.
Keywords
• Fractional calculusImportant Dates:
Deadline for manuscript submissions: : 31 December 2021
The direct link for the submission of papers is https://www.mdpi.com/journal/mathematics/special_issues/Fractional_Calculus_Magnetic_Resonance.
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Books
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Fractional Differential Equations: Finite Difference Methods
(Authors:Zhi-Zhong Sun, Guang-hua Gao)
Details:https://doi.org/10.1515/9783110616064
Book Description：
Starting with an introduction to fractional derivatives and numerical approximations, this book presents finite difference methods for fractional differential equations, including time-fractional sub-diffusion equations, time-fractional wave equations, and space-fractional differential equations, among others. Approximation methods for fractional derivatives are developed and approximate accuracies are analyzed in detail.
• A unique overview of finite difference methods for fractional differential equations.
• Supplied with numerous examples to facilitate understanding.
• Of interest to applied mathematicians and physicists as well as to engineers.
Readership:
Researchers and graduate students in mathematics, physics, and engineering.
Contents:
-Frontmatter
-Preface
-Contents
-Fractional derivatives and numerical approximations
-Difference methods for the time-fractional subdiffusion equations
-Difference methods for the time-fractional wave equations
-Difference methods for the space-fractional partial differential equations
-Difference methods for the time-space-fractional differential equations
-Difference methods for the time distributed-order subdiffusion equations
-A The Matlab code of sum-of-exponentials approximations for the kernel t−α in the Caputo fractional derivative
-Bibliography
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Journals
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Fractional Calculus and Applied Analysis
(Volume 23 Issue 5)
Tempered relaxation equation and related generalized stable processes
Luisa Beghin and Janusz Gajda
Integrability properties of integral transforms via morrey spaces
Natasha Samko
Fractional integro-differential equations in Wiener spaces
Vu Kim Tuan
J.A. Tenreiro Machado and Daniel Cao Labora
Two high-order time discretization schemes for subdiffusion problems with nonsmooth data
Yanyong Wang, Yubin Yan, and Yan Yang
Kangqun Zhang
Palanisamy Duraisamy, Thangaraj Nandha Gopal, and Muthaiah Subramanian
Regularity results for nonlocal evolution Venttsel’ problems
Simone Creo, Maria Rosaria Lancia, and Alexander I. Nazarov
Multivariate fractional phase–type distributions
Hansjörg Albrecher, Martin Bladt, and Mogens Bladt
Trace inequalities for fractional integrals in mixed norm grand lebesgue spaces
Vakhtang Kokilashvili and Alexander Meskhi
The asymptotic behavior of solutions of discrete nonlinear fractional equations
Mustafa Bayram, Aydin Secer, and Hakan Adiguzel
State dependent versions of the space-time fractional poisson process
Kuldeep Kumar Kataria and Palaniappan Vellaisamy
Yatian Pei and Yong-Kui Chang
Experimental investigation of fractional order behavior in an oscillating disk
Richard Mark French, Rajarshi Choudhuri, Jose Garcia-Bravo, and Jordan Petty
Cauchy problem for general time fractional diffusion equation
Chung-Sik Sin
(Selected)
Fractional damping enhances chaos in the nonlinear Helmholtz oscillator
Adolfo Ortiz, Jianhua Yang, Mattia Coccolo, Jesús M. Seoane, Miguel A. F. Sanjuán
Nonexistence of invariant manifolds in fractional-order dynamical
Sachin Bhalekar, Madhuri Patil
Stability analysis of switched fractional-order continuous-time systems
Tian Feng, Lihong Guo, Baowei Wu, Yangquan Chen
Adaptive fixed-time control for Lorenz systems
Huanqing Wang, Hanxue Yue, Siwen Liu, Tieshan Li
Noise effect on the signal transmission in an underdamped fractional coupled system
Suchuan Zhong, Lu Zhang
Sen Zhang, Jiahao Zheng, Xiaoping Wang, Zhigang Zeng, Shaobo He
The direct method of Lyapunov for nonlinear dynamical systems with fractional damping
Matthias Hinze, André Schmidt, Remco I. Leine
A novel chaotic map constructed by geometric operations and its application
Zhiqiang Zhang, Yong Wang, Leo Yu Zhang, Hong Zhu
Primary and subharmonic simultaneous resonance of fractional-order Duffing oscillator
Yongjun Shen, Hang Li, Shaopu Yang, Mengfei Peng, Yanjun Han
Nonlinear vibrations and damping of fractional viscoelastic rectangular plates
Marco Amabili, Prabakaran Balasubramanian, Giovanni Ferrari
Asymptotic stabilization of general nonlinear fractional-order systems with multiple time delays
Zhang Zhe, Zhang Jing
Hui Zhang, Xiaoyun Jiang
On fractional difference logistic maps: Dynamic analysis and synchronous control
Yupin Wang, Shutang Liu, Hui Li
Mohamed El-Borhamy
Stability of fractional-order systems with Prabhakar derivatives
Roberto Garrappa, Eva Kaslik
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Paper
Highlight
Towards a unified approach to nonlocal elasticity via fractional-order mechanics
Sansit Patnaik, Sai Sidhardh, Fabio Semperlotti
Publication information: International Journal of Mechanical Sciences, Volume 189, 1 January 2021, 105992
https://doi.org/10.1016/j.ijmecsci.2020.105992
Abstract
This study presents a fractional-order continuum mechanics approach that allows combining selected characteristics of nonlocal elasticity, typical of classical integral and gradient formulations, under a single frame-invariant framework. The resulting generalized theory is capable of capturing both stiffening and softening effects and it is not subject to the inconsistencies often observed under selected external loads and boundary conditions. The governing equations of a 1D continuum are derived by continualization of the Lagrangian of a 1D lattice subject to long-range interactions. This approach is particularly well suited to highlight the connection between the fractional-order operators and the microscopic properties of the medium. The approach is also extended to derive, by means of variational principles, the governing equations of a 3D continuum in strong form. The positive definite potential energy, characteristic of our fractional formulation, always ensures well-posed governing equations. This aspect, combined with the differ-integral nature of fractional-order operators, guarantees both stability and the ability to capture dispersion without requiring additional inertia gradient terms. The proposed formulation is applied to the static and free vibration analyses of either Timoshenko beams or Mindlin plates. Numerical results, obtained by a fractional-order finite element method, show that the fractional-order formulation is able to model both stiffening and softening response in these slender structures. The numerical results provide the foundation to critically analyze the physical significance of the different fractional model parameters as well as their effect on the response of the structural elements.
Highlights
• Fractional-order continuum formulation that captures both stiffening and softening effects.
• Frame-invariant 3D model developed starting from a 1D lattice with long-range interactions.
• Well-posed nonlocal governing equations derived from a positive definite system.
• Predicts anomalous attenuation-dispersion characteristics within a causal framework.
• Static and free vibration response of Timoshenko beams and Mindlin plates analyzed.
Keywords
Fractional calculus; Nonlocal elasticity; Strain-gradient elasticity; Stiffening; Softening
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Hong Guang Sun, Zhaoyang Wang, Jiayi Nie, Yong Zhang, Rui Xiao
Publication information: Computational Mechanics, 12 September 2020
https://doi.org/10.1007/s00466-020-01917-y
Abstract
Fractional diffusion equations have been widely used to accurately describe anomalous solute transport in complex media. This paper proposes a local meshless method named the generalized finite difference method (GFDM), to solve a class of multidimensional space fractional diffusion equations (SFDEs) in a finite domain. In the GFDM, the spatial derivative terms are expressed as linear combinations of neighboring-node values with different weighting coefficients using the moving least-square approximation. An explicit formula for the SFDE is then obtained. The numerical solution is achieved by solving a sparse linear system. Four numerical examples are provided to verify the effectiveness of the proposed method. Numerical analysis indicates that the relative errors of prediction results are stable and less than 1% (0.001–1%). The method can also be applied for irregular grids with acceptable accuracy.
Keywords:
Space fractional diffusion equations; Generalized finite difference method; Local meshless method; Moving least-square approximation
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