FDA Express Vol. 57, No. 2
FDA Express Vol. 57, No. 2, Nov. 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
For subscription: http://jsstam.org.cn/fda/subscription.htm
PDF download: http://em.hhu.edu.cn/fda/Issues/FDA_Express_Vol 57_No 2_2025.pdf
◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Recent Trends in Fractional Integral and Derivative Operators
Numerical Solution and Applications of Fractional Differential Equations, 3rd Edition
◆ Books Fractional Derivatives for Physicists and Engineers, Volume II Applications ◆ Journals Mathematics and Computers in Simulation ◆ Paper Highlight
Dynamics of Bedload Anomalous Transport: A Nonstationary Lévy Stochastic Process and Upscaling Model
Fractional differential equations via Fourier transform and curvilinear cuts in the complex plane
◆ Websites of Interest Fractal Derivative and Operators and Their Applications Fractional Calculus & Applied Analysis ======================================================================== Latest SCI Journal Papers on FDA －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Hölder regularity for nonlocal in time subdiffusion equations with general kernel
Kubica, A; Ryszewska, K and Zacher, R
JOURNAL OF DIFFERENTIAL EQUATIONS Volume: 450 Published: Jan 2026
A nonlocal dispersive optimal transport: Formulation and algorithm
Bai, SH; Guo, X; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 476 Published: Apr 2026
A fractional partition of unity finite element method for transient anomalous diffusion problems
Achabbak, A; Mohamed, MS; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 474 Published: Mar 2026
Liu, XJ; Deng, K and Luo, MK
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 152 Published: Jan 2026
Anomalous diffusion in nonlocal media via distributed-order fractional operators
Khachnaoui, K
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 152 Published: Jan 2026
Space-time fractional diffusion with stochastic resetting
Priti and Kumar, A
STATISTICS & PROBABILITY LETTERS Volume: 476 Published: Jan 2026
Wu, HH and Yang, HQ
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 475 Published: Jan 2026
Warbhe, U
ANNALS OF NUCLEAR ENERGY Volume: 225 Published: Jan 2026
A normalized variable-order time-fractional diffusion equation
Lee, C and Kim, J
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS Volume: 680 Published: Dec 2026
Ilyas, A and Serra-Capizzano, S
APPLIED MATHEMATICS AND COMPUTATION Volume: 507 Published: Dec 2025
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
Ahmad, J; Masood, K; etc.
HIGH ENERGY DENSITY PHYSICS Volume: 57 Published: Dec 2025
Efficient numerical simulation of variable-order fractional diffusion processes with a memory kernel
Bera, S; Sen, M and Nath, S
JOURNAL OF COMPUTATIONAL SCIENCE Volume: 92 Published: Dec 2025
Priyanka and Kumar, S
COMPUTERS & MATHEMATICS WITH APPLICATIONS Volume: 199 Published: Dec 2025
Wang, J; Xue, T and Zhang, XB
INTERNATIONAL COMMUNICATIONS IN HEAT AND MASS TRANSFER Volume: 169 Published: Dec 2025
Han, TY; Jiang, YY and Fan, HG
AIN SHAMS ENGINEERING JOURNAL Volume: 16 Published: Nov 2025
Time fractional-integer hybrid modeling for anomalous thermal contact problems
Wang, J; Xue, T and Zhang, XB
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER Volume: 251 Published: Nov 2025
Chemical Continuous Time Random Walks under Anomalous Diffusion
Zhang, H; Li, GH; etc.
JOURNAL OF STATISTICAL PHYSICS Volume: 192 Published: Nov 2025
Azin, H; Ordokhani, Y and Kashkooly, AI
JOURNAL OF SUPERCOMPUTING Volume: 81 Published: Nov 2025
========================================================================== Call for Papers －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Recent Trends in Fractional Integral and Derivative Operators
( A special issue of Fractal and Fractional)
Dear Colleagues,
The behavior of numerous dynamic systems, including diffusion processes, milling processes, data networks, transportation, plasma physics, Lévy processes, economics, flexible structures, and continuum robots, is often effectively described using fractional operators. Operators like fractional derivatives and integrals are essential for capturing the complex dynamics and memory effects in these systems. Fractional-order models are particularly useful for systems with long-term memory, hereditary effects, and nonlocal interactions, providing a more accurate description than traditional local models.
We are pleased to announce a Special Issue titled “Recent Trends in Fractional Integral and Derivative Operators”, which aims to highlight the latest developments, methodologies, and applications of fractional calculus in control theory and the modeling of dynamical systems. This Special Issue provides a platform for researchers to explore and discuss developments in the use of fractional integrals and derivatives across a wide range of systems.
We invite original research articles and reviews that explore various aspects of fractional-order systems, including but not limited to, the following research areas:
• Fractional-order systems and their theoretical foundations.
• Applications of fractional derivatives in diffusion and random walk processes.
• Time-delay systems involving fractional integrals and derivatives.
• Fractional calculus in control theory, including modeling and stability analysis.
• Stochastic systems and Lévy processes modeled with fractional operators.
• Numerical methods for solving fractional differential equations.
• The role of fractional operators in modeling physical and engineering systems.
Organizers:
Dr. Arman Dabiri
Important Dates:
Deadline for conference receipts: 10 December 2025.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/Z6UUEOPTMK.
Numerical Solution and Applications of Fractional Differential Equations, 3rd Edition
( A special issue of Fractal and Fractional )
Dear Colleagues,
Over the last few decades, the application of fractional calculus to real-world problems has grown rapidly, in which the use of dynamical systems described by fractional differential equations (FDEs) had been one of the ways to understand complex materials and processes. Due to the power to model the non-locality, memory, spatial heterogeneity, and anomalous diffusion inherent in many real-world problems, the application of FDEs has been attracting much attention in many fields of science and is still under development. However, generally, the fractional mathematical models from science and engineering are so complex that analytical solutions are not available. Therefore, the numerical solution has been an effective tool to deal with fractional mathematical models.
This Special Issue aims to promote communication between researchers and practitioners on the application of fractional calculus, present the latest development of fractional differential equations, report state-of-the-art and in-progress numerical methods, and discuss future trends and challenges. We cordially invite you to contribute by submitting original research articles or comprehensive review papers. This Special Issue will cover, but is not limited to, the following topics:
• Mathematical modeling of fractional dynamic systems;
• Analytical or semi-analytical solution of fractional differential equations;
• Numerical methods to solve fractional differential equations, e.g., the finite difference method, the finite element method, the finite volume method, the spectral method, etc.;
• Fast algorithm for the time- or space-fractional derivative;
• Mathematical analysis for fractional problems and numerical analysis for the numerical scheme;
• Applications of fractional calculus in physics, biology, chemistry, finance, signal and image processing, hydrology, non-Newtonian fluids, etc.
Organizers:
Dr. Libo Feng Important Dates: Deadline for manuscript submissions: 25 December 2025. All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/NHLN0JKWF6. =========================================================================== Books －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Fractional Derivatives for Physicists and Engineers, Volume II Applications ( Authors: Vladimir V. Uchaikin) Details: https://doi.org/10.1007/978-981-96-0582-8 Book Description: This book brings new perspectives in front of the reader dealing with turbulence and semiconductors, plasma and thermodynamics, mechanics and quantum optics, nanophysics and astrophysics. The first derivative of a particle coordinate means its velocity, the second means its acceleration, but what does a fractional order derivative mean? Where does it come from, how does it work, where does it lead to? The two-volume book written on high didactic level answers these questions. The first volume (ISBN: 978-3-642-33910-3) contains a clear introduction into such a modern branch of analysis as fractional calculus. This second volume develops a wide panorama of applications of the fractional calculus to various physical problems. Author Biography: Department of Theoretical Physics, Ulyanovsk State University, Ulyanovsk, Russia Contents: ======================================================================== Journals －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Mathematics and Computers in Simulation (Selected) (Selected) ======================================================================== Paper Highlight Dynamics of Bedload Anomalous Transport: A Nonstationary Lévy Stochastic Process and Upscaling Model ZhiPeng Li, HongGuang Sun Publication information: Water Resources Research, Volume 61, 20 November 2025. https://doi.org/10.1029/2025WR041369 Abstract Anomalous bedload transport has been widely observed in both laboratory settings and natural rivers. Previous studies have utilized the fractional advection‐diffusion equation (FADE) model to characterize the observed anomalous bedload transport behaviors, with the model's parameters being determined by the tail distributions of the probability density functions (PDFs) for particle resting times and step lengths. FADE model captures sub‐diffusion and super‐diffusion behavior resulting from the heavy‐tailed PDFs of step lengths and resting times; however, it overlooks the temporal variability of advection and diffusion coefficients throughout the transport process. This study developes a novel microscopic stochastic process that incorporates nonstationary Lévy motion. The scaling limit of the stochastic process leads to the development of a hybrid Hausdorff‐fractional model. In the upscaling model, sub‐diffusion is represented by a time‐metric transformation, while super‐diffusion is characterized by nonlocal particle movements. Applications show that the novel model serves a generalized tool to characterize anomalous bedload transport processes across various scales. The upscaling model bridges the microscopic stochastic particle dynamics and macroscopic bedload transport behavior, and the microscopic stochastic framework provides a comprehensive physical interpretation for each parameter in the macroscopic equations, thereby enhancing the understanding of collective particle dynamics. Key Points A novel upscaling model is proposed by incorporating a nonstationary Lévy motion －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Zhien Li, Chao Wang, Li Yang Publication information: Fractional Calculus and Applied Analysis, Volume 28, 11 November 2025. Abstract In this paper, based on the notion of the operator of complex fractional derivative proposed by P. Závada [Commun. Math. Phys. 192 (1998), pp.261-285], we introduce a new class of fractional differential equations in the complex plane which allows the complex constant delay. By virtue of classifying the curvilinear cuts, the corresponding integral representations for the fractional differential equations are obtained under the effective integral paths. Meanwhile, the trajectories of the motion paths of the complex constant delays along all types of branch cuts in the complex plane are characterized. We demonstrate that not all branch cuts are suitable for discussing the complex delay fractional differential equations and analyze the geometric paths of these branch cuts in which the effective paths can be selected under our established sufficient conditions. Based on it, the existence, uniqueness and continuation theorems of complex delay fractional differential equations are established along the directions of the curvilinear cuts. Keywords Complex delay fractional differential equations; Fourier transform; Curvilinear cuts; Existence and uniqueness; Continuation ========================================================================== The End of This Issue ∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽
Prof. Dr. Yang Liu
Dr. Lin Liu
This book is addressed to students, engineers and physicists, specialists in theory of probability and statistics, in mathematical modeling and numerical simulations, to everybody who doesn't wish to stay apart from the new mathematical methods becoming more and more popular.
Mechanics
Continuum Mechanics
Porous Media
Thermodynamics
Electrodynamics
Quantum Mechanics
Plasma Dynamics
Cosmic Rays
Closing Chapter
Back Matter
Numerical analysis of a positivity-preserving finite element method for fractional Fisher–KPP equation
Zichen Yao, Zhanwen Yang, Mingying Sun
A numerical method for the solution of the two-dimensional time-fractional cable equation of distributed-order involving Riesz space-fractional operators
M. H. Derakhshan, H. R. Marasi, Pushpendra Kumar
Adaptive spectral solver for Riesz fractional reaction–diffusion equations via penalized minimum residual iteration
Chaoyue Guan, Jian Zhang
An efficient parallel algorithm for solving viscoelastic wave equations
Yaomeng Li, Xu Guo
High-order numerical method for Caputo–Hadamard fractional reaction-diffusion equations using nonuniform temporal mesh
Siyuan Chen, Hengfei Ding
Averaging principle for stochastic fractional differential equations driven by Tempered Fractional Brownian Motion with two-time-scale Markov switching
Hengzhi Zhao, Qin Wu, etc.
An improved meshless finite integration method for the time fractional diffusion and high order equations
Pengyuan Liu, Min Lei, Yiu-Chung Hon
Asymptotic behavior of solutions of a time–space fractional diffusive Volterra equation
Mokhtar Kirane, Sofwah Ahmad
Asymptotically period doubling bifurcation of fractional difference equations
Hu-Shuang Hou, Guo-Cheng Wu, etc.
Fast linearized compact difference scheme for a two-dimensional nonlinear time-fractional diffusion-wave equation
Meng Wang, Lijuan Nong, An Chen
Lattice Boltzmann method with diffusive scaling for space-fractional Navier-Stokes equations
Junjie Ren, Xiaoli Yang
Application of -fractional Genocchi wavelets for solving -fractional differential equationsχχ
Parisa Rahimkhani, Thabet Abdeljawad
An efficient Newton-ADI scheme for 2D time-fractional reaction–diffusion equations with weak initial singularity
Deeksha Singh, Rajesh K. Pandey
Nonuniform L1/spectral element algorithm for the time fractional diffusion equation
Min Cai, Weiwei Tong
Singularity-removing Chebyshev collocation methods for nonlinear fractional differential equations with blow-up
Chengwang Jia, Hongwei Zhang, etc.
Internal resonance analysis and parameter optimization of the fractional SD oscillator system
Xuan Luo, Jiaquan Xie, Wei Shi, etc.
Nonlinear hemodynamics modeling of fractional Jeffery ternary hybrid nanofluid flow in multi-stenosed arteries with ANN-based simulation
Chandrakanta Parida, Ganeswar Mahanta, Sachin Shaw
Design of stochastic backpropagative autoregressive exogenous neuroarchitectures for predictive analysis of fractional-order nonlinear Rabinovich–Fabrikant chaotic attractors
Shahzaib Ahmed Hassan, Muhammad Junaid Ali Asif Raja, Syed Zoraiz Ali Sherazi, etc.
Unraveling memory effects and chaos control in a fractional-order tri-trophic food web: insights from iso-spike patterns in bi-parametric plane
Anuj Kullu, Prajjwal Gupta, Anupam Priyadarshi
Internal resonance analysis and parameter optimization of the fractional SD oscillator system
Xuan Luo, Jiaquan Xie, Wei Shi, etc.
Fuzzy adaptive output-feedback control for incommensurate fractional-order nonlinear systems with input and output quantization
Zhiyao Ma, Ke Sun, Hongjun Ma
Hybrid GA-IPA and neural network-based solution for fractional-order nonlinear predator-prey dynamical systems
Nassira Madani, Zakia Hammouch, Necati Ozdemir
Generalized fractional integrals based on the Rathie I-function as a kernel
Virginia Kiryakova
Nonlinear control-based quasi-synchronization and adaptive synchronization of fully complex-valued uncertain fractional-order competitive neural networks
Shenglong Chen, Zhiming Li, Leimin Wang, etc.
Dynamic stability of a fractional-order hydropower generation system with hydraulic-mechanical–electrical structure in the load rejection transient process
Huanhuan Li, Huiyang Jia, Beibei Xu, etc.
Multipole solitons of fractional second-third order nonlinear Schrödinger system with PT symmetric potential
Tong-Zhen Xu, Jin-Hao Liu, Chao-Qing Dai, etc.
Analysis of fractional order SVEIR infectious disease model with fear effect and secondary vaccination
Jinyu Zhang, Yakui Xue & Guoqing Hu
FractionalNet: a symmetric neural network to compute fractional-order derivatives
Dhanush Biligiri, Jack Anders Smitterberg, Shivayogi Akki, etc.
Delayed duffing equation with fractional order damping
Nahid Hida, Faouzi Lakrad
Models of nonlinear higher-order elements for autonomous fractional circuits
Dalibor Biolek, Ivo Petráš
The sub- and super-diffusion behaviors are simultaneously characterized by a time-metric transformation and nonlocal particle movement
A novel upscaling model bridges the microscopic stochastic particle dynamics and macroscopic bedload transport behavior
Fractional differential equations via Fourier transform and curvilinear cuts in the complex plane
https://doi.org/10.1007/s13540-025-00466-6
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