FDA Express Vol. 57, No. 1
FDA Express Vol. 57, No. 1, Oct. 31, 2025
All issues: http://www.jsstam.org.cn/?list_65/
Editors: http://jsstam.org.cn/fda/Editors.htm
Institute of Soft Matter Mechanics, Hohai University
For contribution: xybxyb@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 57_No 1_2025.pdf
◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Recent Advances in the Spatial and Temporal Discretizations of Fractional PDEs, Second Edition
Recent Advances in Fractional Fourier Transforms and Applications, 2nd Edition
◆ Books Optimal Stability Theory and Approximate Solutions of Fractional Systems ◆ Journals Fractional Calculus and Applied Analysis ◆ Paper Highlight
Deep learning for high-dimensional PDEs with fat-tailed Lévy measure
◆ Websites of Interest Fractal Derivative and Operators and Their Applications Fractional Calculus & Applied Analysis ======================================================================== Latest SCI Journal Papers on FDA －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Chen, C; Yang, X and Zhang, FY
APPLIED MATHEMATICS AND COMPUTATION Volume: 510 Published: Feb 2026
The spreading phenomenon of solutions for reaction-diffusion equations with fractional Laplacian
Ma, LY; Niu, HT and Wang, ZC
APPLIED MATHEMATICS LETTERS Volume: 172 Published: Jan 2026
Singh, D and Pandey, RK
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 240 Published: Feb 2026
Yang, F; Yan, LL and Li, XX
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 476 Published: Apr 2026
Edward, J
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 556 Published: Apr 2026
Abali, S and Konuralp, A
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 476 Published: Apr 2026
Halder, S; Deepmala and Agarwal, RP
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 475 Published: Mar 2026
Ou, CX; Wang, ZB and Vong, S
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 475 Published: Mar 2026
Hu, DD; Chen, MH; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 475 Published: Mar 2026
Zhao, HZ; Wu, Q; etc.
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 241 Published: Mar 2026
Inhomogeneous generalized fractional Bessel differential equations in complex domain
Yadav, B; Mathur, T and Agarwal, S
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 555 Published: Mar 2026
Liu, PY; Lei, M and Hon, YC
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 241 Published: Mar 2026
Aghaei, AA; Nejad, AG; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 474 Published: Mar 2026
Abbasbandy, S
APPLIED MATHEMATICS AND COMPUTATION Volume: 511 Published: Feb 2026
Melo, WG
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 554 Published: Feb 2026
Asymptotic behavior of solutions of a time-space fractional diffusive Volterra equation
Kirane, M and Ahmad, S
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 240 Published: Feb 2026
Numerical solution of time fractional KdV equation using a dual-Petrov-Galerkin approximation
Fakhari, H and Mohebbi, A
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 473 Published: Feb 2026
Zhang, XY; Hao, ZC and Bohner, M
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS Volume: 87 Published: Feb 2026
Comparison results for the fractional heat equation with a singular lower order term
Brandolini, B; de Bonis, I; etc.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS Volume: 87 Published: Feb 2026
========================================================================== Call for Papers －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Recent Advances in the Spatial and Temporal Discretizations of Fractional PDEs, Second Edition
( A special issue of Fractal and Fractional)
Dear Colleagues,
Fractional PDEs (FPDEs) generalize the classic (integer-order) calculus and PDEs to any differential form of fractional orders. FPDEs are emerging as a powerful tool for modeling challenging multiscale phenomena, including overlapping microscopic and macroscopic scales, anomalous transport and long-range time–memory or spatial interactions. However, the exact solutions of FPDEs cannot be explicitly expressed; thus, numerical methods based on various spatial and temporal discretizations have become the mainstream tools for such FPDEs and have experienced a drastic development in recent decades. These spatial and temporal discretizations that maintain the important characteristics or structures of FPDEs, such as weak singularity, optimal long-time decay rate, long-term numerical stability and the convergence of numerical schemes for such FPDEs, are still limited. Therefore, developing efficient spatial and temporal discretizations for the numerical solutions of FPDEs remains challenging in the field of numerical analysis.
This Special Issue, titled “Recent Advances in the Spatial and Temporal Discretizations of Fractional PDEs, Second Edition”, will provide a platform for recent and original research results on efficient numerical methods for solving FPDEs. We invite authors to contribute original research articles on topics including, but not limited to, the following:
• Finite difference, finite elements, finite volume and spectral methods;
• Nonuniform and adaptive discretizations;
• Adaptive space–time methods;
• Numerical treatments of integro-differential equations;
• Parallel-in-time methods;
• Fast matrix computations arising from numerical methods for FPDEs;
• Nonlocal modeling and computation;
• Convolution quadrature;
• Modeling and simulations involving (fractional) PDEs.
Organizers:
Dr. Xian-Ming Gu
Prof. Dr. Hongbin Chen
Prof. Dr. Xiangcheng Zheng
Important Dates:
Deadline for conference receipts: 14 November 2025.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/J6C38072M9.
Recent Advances in Fractional Fourier Transforms and Applications, 2nd Edition
( A special issue of Fractal and Fractional )
Dear Colleagues,
With the rapid development of modern signal processing theory, the processed signal has gradually developed from the early stationary signal to the non-stationary, non-Gaussian, non-single sampling complex signal. As one of the important branches of non-stationary signal processing theory, fractional Fourier transform (FRFT) is favored by many researchers due to its unique characteristics. In recent decades, new research results have emerged in an endless stream. FRFT has been widely used in many scientific research and engineering fields, such as swept filters, artificial neural networks, wavelet transform, time–frequency analysis, time-varying filtering, complex transmission, partial differential equations, quantum mechanics, etc. In addition, FRFT can also be used to define fractional convolution, correlation, Hilbert transform, Riesz transform, and other operations, and can also be further generalized into the linear canonical transformation.
This Special Issue aims to continue to advance research on topics relating to the theory, algorithm development, and application of fractional Fourier transform.
Topics that are invited for submission include (but are not limited to):
• Mathematical theory of FRFT;
• Fractional integral transformation based on FRFT, such as Hilbert transform, Riesz transform;
• Applications of FRFT in signal processing, PDE, information security, and other fields;
• Numerical algorithm of FRFT;
• The generalization of FRFT (e.g., the linear canonical transform (LCT), fractional wavelet transforms, and chirp Fourier transform) in theory and applications.
Organizers:
Prof. Dr. Zunwei Fu Important Dates: Deadline for manuscript submissions: 25 November 2025. All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/FRFT_II. =========================================================================== Books －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Optimal Stability Theory and Approximate Solutions of Fractional Systems ( Authors: Zahra Eidinejad, Reza Saadati, Tofigh Allahviranloo, Chenkuan Li, Javad Vahidi) Details: https://doi.org/10.1007/978-3-031-96704-7 Book Description: This comprehensive book is designed for undergraduate, master's, and doctoral students in mathematics, as well as scholars interested in a deep understanding of fractional problems. The book covers a wide range of topics, including the existence and uniqueness of solutions, stability, optimal controllers, special functions, classical and fuzzy normed spaces, matrix functions, fuzzy matrix normed spaces, fixed-point theory, quality and certainty, and various numerical methods. Author Biography: Iran University of Science and Technology, Tehran, Iran Contents: ======================================================================== Journals －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Fractional Calculus and Applied Analysis (Volume 28, Issue 5) (Selected) ======================================================================== Paper Highlight A spatio-temporal radial basis function collocation method based on Hausdorff fractal distance for Hausdorff derivative heat conduction equations in three-dimensional anisotropic materials Jiayu Wang, Lin Qiu, Yingjie Liang, Fajie Wang Publication information: Applied Mathematics and Computation, Volume 502, October 2025. https://doi.org/10.1016/j.amc.2025.129501 Abstract In this paper, the spatio-temporal radial basis function (RBF) collocation method based on Hausdorff fractal distance is developed and used to simulate the transient heat transfer problems in anisotropic materials governed by Hausdorff derivative heat conduction equations. We introduce Hausdorff fractal distance into the conventional RBFs, and based on this incorporation, establish a meshless method to address Hausdorff derivative heat conduction problems, in which the anisotropy of the thermal conductivity of the material and spatio-temporal fractal characteristics are taken into account. We set the source points of the collocation method outside the spatial computational domain instead of distributing them within the original domain to further improve the accuracy of the method. Numerical experiments carried out in this study demonstrate the superior performance of the proposed approach compared to the finite element method and traditional RBF collocation method, showing that the developed method can be considered as a competitive tool for simulating Hausdorff derivative transient heat conduction problems in complex geometries. Keywords Radial basis function; Hausdorff derivative; Spatio-temporal approach; Hausdorff fractal distance; Anisotropic heat conduction －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Kamran Arif, Guojiang Xi, Heng Wang, Weihua Deng Publication information: Journal of Computational Physics, Volume 541, 5 November 2025. Abstract The partial differential equations (PDEs) for jump process with Lévy measure have wide applications. When the measure has fat tails, it will bring big challenges for both computational cost and accuracy. In this work, we develop a deep learning method for high-dimensional PDEs related to fat-tailed Lévy measure, which can be naturally extended to the general case. Building on the theory of backward stochastic differential equations for Lévy processes, our deep learning method avoids the need for neural network differentiation and introduces a novel technique to address the singularity of fat-tailed Lévy measures. The developed method is used to solve four kinds of high-dimensional PDEs: the diffusion equation with fractional Laplacian; the advective diffusion equation with fractional Laplacian; the advective diffusion reaction equation with fractional Laplacian; and the nonlinear reaction diffusion equation with fractional Laplacian. The parameter β in fractional Laplacian is an indicator of the strength of the singularity of Lévy measure. Specifically, for β∈(0,1), the model describes super-ballistic diffusion; while for β∈(1,2), it characterizes super-diffusion. In addition, we experimentally verify that the developed algorithm can be easily extended to solve fractional PDEs with finite general Lévy measures. Our method achieves a relative error of O(10^(-3)) for low-dimensional problems and O(10^(-2)) for high-dimensional ones. We also investigate three factors that influence the algorithm’s performance: the number of hidden layers; the number of Monte Carlo samples; and the choice of activation functions. Furthermore, we test the efficiency of the algorithm in solving problems in 3D, 10D, 20D, 50D, and 100D. Our numerical results demonstrate that the algorithm achieves excellent performance with deeper hidden layers, a larger number of Monte Carlo samples, and the Softsign activation function. Keywords Jump process; Fat-tailed Lévy measure; Fractional Laplacian; BSDE; Deep learning ========================================================================== The End of This Issue ∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽
Prof. Dr. Bingzhao Li
Dr. Xiangyang Lu
The primary objective of this book is to analyze the existence and uniqueness of solutions for functional equations, analyze stability, and achieve the best possible results with minimal error. With a clear and direct approach, it presents advanced concepts in an accessible and comprehensible manner, enabling students to apply their knowledge to solving various problems.
To prevent instability in fractional systems, methods based on fixed-point theory with the best approximation have been utilized. The stability analysis of fractional equations is conducted by considering classical and fuzzy normed spaces and employing special functions as optimal controllers. In fuzzy systems, the Z-number theory has been used to enhance results and improve quality. This theory enables the assessment of approximation accuracy and quality, providing the best possible approximation.
The numerical analysis of fractional systems plays a crucial role in accurately modeling physical phenomena, simulations, and predicting complex systems. By presenting numerical results from fractional systems, which are essential in solving real-world problems and optimizing computational algorithms, this book serves as a valuable resource for both researchers and students.
Faculty of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, Iran
Vadi Campus, Istinye University in Istanbul, Istanbul, Türkiye
Mathematics and Computer Science, Brandon University, Brandon, Canada
Faculty of Mathematics and Computer Science, Iran University of Science and Technology, Tehran, Iran
Basic Concepts Review
Analysis of a New Stability
Analysis of a New Stability on Matrix Valued Fuzzy Spaces
Picard Method
Cellular Neural Networks, Pseudo Almost Automorphic Solution
Z-Numbers
Analysis of Numerical Methods
Multiple solutions for anisotropic nonlocal problems with variable exponents
Elhoussine Azroul, Nezha Kamali, etc.
Existence and uniqueness of mild solutions for a class of psi-Caputo time-fractional systems of order from one to two
Hamza Ben Brahim, Fatima-Zahrae El Alaoui, etc.
Inverse problem to determine simultaneously several scalar parameters and a time-dependent source term in a superdiffusion equation involving a multiterm fractional Laplacian
Hany Gerges, Jaan Janno
Measure attractors of asymptotic autonomy fractional stochastic reaction-diffusion equations on unbounded domains
Ran Li, Peter E. Kloeden, Dingshi Li
Finding extrema using the unified fractional derivative: a conjecture
Manuel D. Ortigueira
Topological properties of solution sets for control problems driven by fractional delay differential quasi-hemivariational inequalities and applications
Yirong Jiang, Xiaoling Qin, Guoji Tang
Approximation by Riemann-Liouville Fractional Kantorovich type Operators
Priya Sehrawat, Arun Kajla
Block generalized Adams convolution quadrature for the backward fractional Feynman-Kac equation
Ling Liu, Jinrong Wang
Comparison principles for the time-fractional diffusion equations with the Robin boundary conditions. Part II: Semilinear equations
Yuri Luchko, Masahiro Yamamoto
Berry-Esséen bounds for the statistical estimators of an Ornstein-Uhlenbeck process driven by a general Gaussian noise
Yong Chen, Ying Li, Hongjuan Zhou
A simple series representation for a class of fractal interpolation functions
Dah-Chin Luor, Chiao-Wen Liu
On systems of fractional nonlinear partial differential equations
Ravshan Ashurov, Oqila Mukhiddinova
Remarks on the nonlinear fractional Choquard equation
Vincenzo Ambrosio
On the solutions to a Riemann-Liouville fractional q-derivative boundary value problem
Luís P. Castro
Nonlinear iterated function systems and fractal interpolation functions with Pata-type contractions
Zhong Dai, Shutang Liu
A new fractional Musielak-Sobolev space and Choquard-Kirchhoff double phase problem with singular nonlinearities
Yu Cheng, Zhanbing Bai
Brezis-Nirenberg type problem for fractional sub-Laplacian on the Heisenberg group
Vikram Yallapa Naik, Gaurav Dwivedi
Complete synchronization of discrete-time fractional-order neural networks with leakage and distributed delays
Jianfei Liu, Hong-Li Li, etc.
Fundamental solutions for abstract fractional evolution equations with generalized convolution operators
Carlos Lizama, Marina Murillo-Arcila
Ultraslow diffusion revisited: Logarithmic scaling in single-term fractional diffusion models for anomalous transport of complex systems
Jincheng Dong, Ning Du, Zhiwei Yang
Conservation laws and discrete counterparts for the time-fractional generalized nonlinear Schrödinger equation
Wei Yao, Pin Lyu, Seakweng Vong
A new method for nonlinear Riesz fractional reaction-diffusion equations
Pingrui Wang, Jiabao Yang, etc.
Fixed-time convergence in discrete fractional systems
Jie Ran, Yonghui Zhou
Fast numerical study on spatial nonuniform grids for two-dimensional fractional coupled equations with fractional Neumann boundary conditions
Jiaxue Kang, Wenping Fan, Zhenhao Lu
Time-splitting Fourier spectral method for two-dimensional space fractional Schrödinger–Poisson-Xα model
Pingrui Zhang, Junqing Jia, Xiaoyun Jiang
Application of the LDG method using generalized alternating numerical flux to the fourth-order time-fractional sub-diffusion model
Xindong Zhang, Leilei Wei, Juan Liu
Computational analysis of a normalized time-fractional Fisher equation
Soobin Kwak, Yunjae Nam, etc.
The inverse source problem for a fractional diffusion-wave equation with inexact order: An asymptotically optimal strategy
Dinh Nguyen Duy Hai
Novel Razumikhin-type finite-time stability criteria of fractional nonlinear systems with time-varying delay
Shuihong Xiao, Jianli Li
A class of higher-order time-splitting Monte Carlo method for fractional Allen–Cahn equation
Huifang Yuan, Zhiyuan Hui
Uniqueness of identifying multiple parameters in a time-fractional Cattaneo equation
Yun Zhang, Xiaoli Feng
Lattice Boltzmann method for surface quasi-geostrophic equations with fractional Laplacian
Haoyuan Gong, Tongtong Zhou, etc.
Local modification and analysis of a variable-order fractional wave equation
Shuyu Li, Hong Wang, Jinhong Jia
Deep learning for high-dimensional PDEs with fat-tailed Lévy measure
https://doi.org/10.1016/j.jcp.2025.114327
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