FDA Express Vol. 56, No. 3
FDA Express Vol. 56, No. 3, Sep. 30, 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
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PDF download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol 56_No 3_2025.pdf
◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Fractional Order Systems Modelling and Control
Applied Fractional Calculus in Machine Learning and Biomedical Engineering
◆ Books Solved Exercises in Fractional Calculus ◆ Journals Computers & Mathematics with Applications Applied Mathematics and Computation ◆ Paper Highlight
Approximation by Riemann-Liouville Fractional Kantorovich type Operators
◆ Websites of Interest Fractal Derivative and Operators and Their Applications Fractional Calculus & Applied Analysis ======================================================================== Latest SCI Journal Papers on FDA －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Machine learning to discover discrete fractional chaotic models
Wu, GC; Wu, ZQ and Ji, LH
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 473 Published: Feb 2026
Fatima, N; Ali, A; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 474 Published: MAR 2026
Zhu, Y; Li, KH; etc.
Chaos Solitons & Fractals Volume: 196 Published: Feb 2025
Zhao, SY; Wang, Z and Wei, YB
PHYSICA SCRIPTA Volume: 100 Published: Apr 2025
Zhang, JJ; Chiu, ST; etc.
GEOENERGY SCIENCE AND ENGINEERING Volume: 247 Published: Apr 2025
Yuan, SH; Liu, YQ; etc.
FRACTAL AND FRACTIONAL Volume: 9 Published: Aug 2025
Ye, YL; Fan, HT; etc.
NONLINEAR DYNAMICS Volume: 113 Published: Apr 2025
Yan, XB; Xu, ZQJ and Ma, Z
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 454 Published: Jan 2025
Grey-informed neural network for time-series forecasting
Xie, WL; Zhao, RB; etc.
NEUROCOMPUTING Volume: 649 Published: Oct 2025
Wu, QW; Ma, FY and Wo, WF
MATHEMATICAL METHODS IN THE APPLIED SCIENCES Volume: 14 Published: Sep 2025
Optimizing tomato plant and insect disease control using a fractional model and deep neural networks
Waseem; Faiz, Z; etc.
COMPUTATIONAL BIOLOGY AND CHEMISTRY Volume: 119 Published: Dec 2025
Convolutional neural network-based reduced-order modeling for parametric nonlocal PDEs
Wang, YM; Zhou, SP and Zhang, YZ
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Volume: 444 Published: Sep 2025
Wang, LL; Qiu, CX; etc.
INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 7 Published: Jul 2025
High-order energy stable algorithm for time-fractional Swift-Hohenberg model on graded meshes
Wang, JY; Shen, XQ; etc.
JOURNAL OF SCIENTIFIC COMPUTING Volume: 104 Published: Jul 2025
Tian, WB; Liu, Y and Zhang, YB
JOURNAL OF GEOPHYSICS AND ENGINEERING Volume: 22 Published: Jan 2025
Srati, M; Oulmelk, A; etc.
JOURNAL OF COMPUTATIONAL PHYSICS Volume: 523 Published: Feb 2025
Srati, M; Oulmelk, A; etc.
APPLIED NUMERICAL MATHEMATICS Volume: 208 Published: Feb 2025
Sivalingam, SM; Govindaraj, V and Dubey, S
Engineering Analysis with Boundary Elements Volume: 178 Published: Sep 2025
Neural fractional order differential equations
Sivalingam, SM and Govindaraj, V
EXPERT SYSTEMS WITH APPLICATIONS Volume: 267 Published: Apr 2025
========================================================================== Call for Papers －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Fractional Order Systems Modelling and Control
( A special issue of International Journal of Dynamics and Control)
Many processes in physics, engineering, biology, economics, finance, and other areas, exhibit global behavior characterized by long-range correlations, memory effects, fractality, and power law dynamics. This behavior is well described by fractional calculus (FC), a mathematical tool that extends integrals and derivatives to non-integer orders. The FC, introduced by Leibniz, has evolved from a theoretical concept to a powerful method for modelling and controlling complex dynamical systems. The non-local, history-dependent, and frequency-dependent characteristics of fractional-order (FO) systems make them particularly valuable for capturing real-world behaviors that classical models struggle to handle.
This special issue (SI) aims to present the latest research on FO systems, with a particular focus on their theoretical foundations, modelling techniques, control, and practical applications. It will highlight the growing importance of FC in addressing challenges in various fields, such as complex dynamics, control, signal processing, fluid mechanics, and biological systems.
Topics of interest of the SI include, but are not limited to: • Advances in FC and its computational methods; • New applications of FO systems in science and engineering; • Case studies of FO models in real-world systems; • Fractional control systems; • FO modelling in biological and ecological systems; • Fractional models in economics, finance, and social sciences; • Numerical and experimental validation of FO models; • Fractional systems in the era of big data and machine learning
Organizers:
António M. Lopes
Behrouz Parsa Moghaddam
Important Dates:
Deadline for conference receipts: 31 December 2025.
All details on this conference are now available at: https://link.springer.com/collections/hehbfeafih.
Applied Fractional Calculus in Machine Learning and Biomedical Engineering
( A special issue of Fractal and Fractional )
Dear Colleagues,
The application of fractional calculus in machine learning and biomedical engineering is a novel and rapidly growing area of research. The non-integer-order differentiation and integration offered by FC allow for more accurate modelling of dynamical systems with memory and hereditary properties, which are common in biological systems and complex datasets.
The intersection of FC with ML and BME is an emerging field that promises to revolutionize the way we approach problems in data analysis, signal processing, biomedical system modelling, and control. This Special Issue will provide a comprehensive platform for researchers to present their latest theoretical advances, innovative applications, and practical implementations of FC in these domains.
This special issue aims to bring together cutting-edge research and developments in the application of fractional calculus (FC) to the fields of machine learning (ML) and biomedical engineering (BME). Fractional calculus, an extension of traditional integer-order calculus, offers a powerful framework for describing anomalous dynamics and complex systems. Its non-local and memory-preserving properties have shown significant potential in modelling and solving complex problems that are otherwise intractable with traditional integer-order methods.
Keywords
• Theoretical advances in fractional calculus and their implications for ML and BME.
• Development of fractional-order algorithms for machine learning models.
• Application of FC in the design of neural networks, including deep learning and reinforcement learning.
• Fractional-order systems in biomedical signal processing and image analysis.
• Modelling of biological systems using fractional-order differential equations (FODEs).
• Fractional-order control systems in biomedical devices and robotics.
• Applications of fractional calculus in physiological modelling and bioinformatics.
• Challenges and future directions in the integration of FC with ML and BME.
Organizers:
Dr. Saptarshi Das Important Dates: Deadline for manuscript submissions: 31 October 2025. All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/UBV441G9XO. =========================================================================== Books －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ ( Authors: Edmundo Capelas de Oliveira, Jayme Vaz) Details: https://doi.org/10.1007/978-3-031-88099-5 Book Description: This textbook provides a comprehensive exploration of special functions and fractional calculus, offering a structured approach through solved and proposed exercises. Covering key mathematical concepts such as Mittag-Leffler functions, Kilbas-Saigo functions, and the Erdélyi-Kober fractional integral, it balances theoretical insights with practical applications. Appendices introduce Barnes G-functions and demonstrate the use of Mathematica for fractional calculus, expanding the book’s accessibility. With an updated index and extensive references, this edition serves as a valuable resource for researchers, graduate students, and professionals in applied mathematics and related fields. Author Biography: Department of Applied Mathematics, UNICAMP, Campinas, Brazil Contents: ======================================================================== Journals －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Computers & Mathematics with Applications (Selected) Applied Mathematics and Computation (Selected) ======================================================================== Paper Highlight Continuous and discrete models for the dynamic behaviors description of suspended sediment-fluid system Lian Wang, Yongchao Zhang, Xihua Chu, Hongguang Sun Publication information: Advances in Water Resources, Volume 205, November 2025. https://doi.org/10.1016/j.advwatres.2025.105104 Abstract Dynamic behaviors of suspended sediment-fluid system play an important role in the transport of bedload and the evolution of riverbed, but the related mathematical models are deficient or limited. In this paper, two models, micropolar fluid model and fluid-particle coupling model, are adopted in the dynamic behaviors calculation of the suspended sediment-fluid system in lid-driven cavity. We first establish the discrete solution program for micropolar fluid governing equations, and analyze the dynamic behaviors of suspended sediment-fluid system under different microstructure parameters. Meanwhile, the dynamic behaviors calculations are carried out by CFD-DEM (Computational Fluid Dynamics-Discrete Element Method) numerical method, and the influences of suspended sediment diameter and concentration are investigated. The results show that micropolar fluid model and fluid-particle coupling model can effectively describe the dynamic behaviors of suspended sediment-fluid system. The influences of microstructure parameters and macro-properties of suspended sediment at given range are almost same, suggesting the definite relationships existed between micro- and macro- quantities. Based on the equivalent effects of microstructure parameters to macro-properties of suspended sediment, micropolar fluid model is expected to replace CFD-DEM method completely in the study of the large-scale dynamic behaviors of suspended sediment-fluid system. Keywords Suspended sediment; Micropolar fluid model; CFD-DEM method; Dynamic behaviors; Microstructure parameter －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Priya Sehrawat, Arun Kajla Guang Lin Publication information: Fractional Calculus and Applied Analysis, Volume 28, 29 September 2025. Abstract In this present note, we construct Riemann-Liouville type fractional Stancu-Kantorovich type operators based on two parameters. Firstly, we establish approximation properties using modulus of continuity, Peetre’s K-functionals, Ditzian-Totik modulus of smoothness and Lipschitz class of functions. Further, we study weighted approximation and present a Voronovskaja type theorem, quantitative Voronovskaja type theorem and Grüss Voronovskaja type theorem. Finally, we confirm the validity of our theoretical results by generating graphical representations using the Maple software. Keywords Riemann-Liouville type fractional; Stancu-Kantorovich operators; Lipschitz type class; Voronovskaja type theorem; Grüss Voronovskaja type theorem; Weighted approximation ========================================================================== The End of This Issue ∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽
A Bit of History
Special Functions
Mittag-Leffler Functions
Integral Transforms
Fractional Derivatives
Applications and Add-Ons
Back Matter
Approximation of unknown sources in a time fractional PDE by the optimal ones and their reconstruction
Mourad Hrizi, Ravi Prakash, Antonio André Novotny.
An averaged L1 ADI compact difference scheme for the three-dimensional time-fractional mobile/immobile transport equation with weakly singular solutions
Kai Liu, Haixiang Zhang, Xuehua Yang
Convergence analysis of a fast ADI compact finite difference method for two-dimensional semi-linear time-fractional reaction-diffusion equations with weak initial singularity
Priyanka, Sunil Kumar
Fast method and theoretical study of magnetohydrodynamic flow and heat transfer for fractional Maxwell fluids
Yi Liu
A novel accelerated tempered algorithm with nonuniform time-stepping compact ADI scheme for 2D tempered-fractional nonlinear Schrödinger equations with weak initial singularity
Himanshu Kumar Dwivedi, Rajeev
Numerical analysis of a discontinuous Galerkin method for time-fractional Navier-Stokes-Fokker-Planck equations with weakly singular solutions
Dong Liu, Weihua Deng
A novel numerical method for solving a two-dimensional variable-order time fractional advection-diffusion problem
Saurabh Kumar, Vikas Gupta, Ajay Kumar
A preconditioned fast finite volume method for two-dimensional conservative space-fractional diffusion equations on non-uniform meshes
Yuan Xu, Siu-Long Lei, etc.
An energy-preserving scheme for coupled fractional Gross-Pitaevskii equations based on energy discretization
Jiangming Ma, Xiang Zhang, etc.
H1-norm error analysis of an ADI compact finite difference method for a two-dimensional time-fractional reaction-diffusion equation with variable coefficients
P. Roul, S. N. Khandagale, Jianxiong Cao
Well-posedness and strong convergence analysis of stochastic space-time fractional wave problems driven by fractional Brownian sheet
Yi Yang, Jin Huang, Hu Li
A localized Fourier collocation method for the numerical solution of nonlinear fractional Fisher–Kolmogorov equation
Farzaneh Safari, Ji Lin, Yanjun Duan
Efficient discretization of fractional SPDEs via Galerkin and exponential Euler methods
Minoo Kamrani
Preconditioning techniques and parameterized regular splitting iteration methods for the Riesz distributed-order space-fractional diffusion equations with variable coefficients
Hong Yang, Cheng-Xue Lao
Solving linear and nonlinear Caputo fractional differential equations with a quantum pseudo-spectral approach
Saeid Abbasbandy
Numerical approximation for a stochastic time-fractional cable equation
Qimin Li, Yubin Yan, etc.
Causal state feedback representation for infinite horizon LQ problems of fractional systems
Jianping Huang, Huacheng Zhou
Sine-transform-based fast solvers for Riesz fractional nonlinear Schrödinger equations with attractive nonlinearities
Chao Chen, Xi Yang, Fei-Yan Zhang
Matrix-based evaluation of the fractional Hankel transform by bessel series expansion
Magdy Tawfik Hanna
Solving fuzzy non-homogeneous linear differential systems with piecewise constant arguments involving the short-memory variable-order Caputo fractional derivative
Nguyen Dinh Phu, Lai Van Phut, Ngo Van Hoa
Multistability and global attractivity for fractional-order spiking neural networks
Shuo Zhang, Lu Liu, etc.
Semi-analytical solution and nonlinear characterization analysis of fractional-order nonlinear systems based on the time-domain minimum residual method
Hai-Su Wang, Zhong-Rong Lu, etc.
A Tikhonov-type method for inverse source problems for time-space fractional parabolic equations
Nguyen Van Duc, Thi-Phong Nguyen
Valuation of R&D projects of new energy vehicles based on generalized mixed sub-fractional Brownian motion under fuzzy environment
Weiting Zhang, Guitian He, etc.
Convergence rate of nonlinear delayed neutral McKean-Vlasov SDEs driven by fractional Brownian motions
Shengrong Wang, Jie Xie, Li Tan.
Neural network approximation of the composition of fractional operators and its application to the fractional Euler-Bernoulli beam equation
Anna Nowak, Dominika Kustal, etc.
Structure-preserving compact ADI schemes for the space fractional Klein-Gordon-Schrödinger equations and the dynamic simulation of solitary wave solutions
Li Chai, Yang Liu, etc.
A class of parameter choice rules for fractional Tikhonov regularization scheme in learning theory
Sreepriya P., Denny K.D.G., D. Reddy
Harnessing machine learning for identifying parameters in fractional chaotic systems
Ce Liang, Weiyuan Ma, etc.
Approximation by Riemann-Liouville Fractional Kantorovich type Operators
https://doi.org/10.1007/s13540-025-00448-8
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