FDA Express Vol. 56, No. 2
FDA Express Vol. 56, No. 2, Aug. 31, 2025
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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 2_2025.pdf
◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Variational Problems and Fractional Differential Equations
Fractional Porous Medium Type and Related Equations
◆ Books Boundary Value Problems Advanced Fractional Dynamic Equations on Time Scales ◆ Journals Fractional Calculus and Applied Analysis Applied Mathematical Modelling ◆ Paper Highlight
Dynamics of fractional stochastic diffusive SIRS epidemic model with Lévy noise
◆ 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
Sadek, L; Samei, ME and Hashemi, MS
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 240 Published: Feb 2026
Ahmad, B; Aldhuain, M and Alsaed, A
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS Volume: 88 Published: Apr 2026
Sher, M; Shah, KM; etc.
APPLIED MATHEMATICAL MODELLING Volume: 474 Published: Mar 2026
Kumar, D; Singh, J and Baleanu, D
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 474 Published: Mar 2026
Aghaei, AA; Nejad, AG; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 474 Published: Mar 2026
Alipour, M and Soradi-Zeid, S
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 473 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
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
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
Multicontinuum modeling of time-fractional diffusion-wave equation in heterogeneous media
Bai, HR; Ammosov, D; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 473 Published: Feb 2026
A finite element discretization of fractional problems using graded meshes
Barrios, M; Lombardi, AL and Penessi, C
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 473 Published: Feb 2026
Constantin, L; Giacomoni, J and Warnault, G
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS Volume: 87 Published: Feb 2026
Application of x-fractional Genocchi wavelets for solving x-fractional differential equations
Rahimkhani, P and Abdeljawad, T
MATHEMATICS AND COMPUTERS IN SIMULATION Volume: 239 Published: Jan 2026
Fractional differential equations with continuous variable coefficients and Sonine kernels
Yücel, YG; Fernandez, A and Mahmudov, NI
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 152 Published: Jan 2026
Dong, RM; Zhu, L; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 472 Published: Jan 2026
========================================================================== Call for Papers －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Variational Problems and Fractional Differential Equations
( A special issue of Fractal and Fractional )
Dear Colleagues,
Fractional differential equations are being frequently used in physics, chemistry, biology, probability and finance modelling problems, such as, the ultrarelativistic limits of quantum mechanics, flame propagation, water waves, chemical reactions of liquids and population dynamics, etc. The Calculus of Variations provides a range of tools for the study of fractional differential equations for both mathematical theory and practical applications. The aim of this Special Issue is to present some of the recent developments on the qualitative properties of solutions for variational problems and fractional differential equations. The potential topics concerned with qualitative properties of solutions include, but are not limited to, a priori estimate, existence, non-existence, uniqueness, regularity, symmetry, stability and asymptotic behavior.
Keywords
• variational problems
• fractional differential equations
• priori estimate
• existence, non-existence, and uniqueness
• regularity and symmetry
• stability
• asymptotic behavior
Organizers:
Prof. Dr. Zhisu Liu
Dr. Yu Su
Important Dates:
Deadline for conference receipts: 30 September 2025.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/231VHG5KZJ.
Fractional Porous Medium Type and Related Equations
( A special issue of Fractal and Fractional )
Dear Colleagues,
Many diffusion processes in nature exhibit anomalous behavior and cannot be modeled by classical diffusion equations (e.g., the heat equation), the classical porous medium equation, or by the classical parabolic p-Laplacian equation.
Subdiffusion is an important special case of anomalous diffusive behavior. It has been experimentally observed in many diffusion processes (e.g., diffusion in amorphous semiconductors) that particles diffuse slower than in the classical case, which can be described by Brownian motion and which leads to the heat equation or some nonlinear version of this equation.
Time-fractional porous medium and related equations, however, are suitable to describe such subdiffusion processes.
They are also able to describe many other diffusion processes where memory effects play a substantial role. These include heat conduction in materials with memory or diffusion processes in porous media with memory effects.
The aim of this volume is to present recent results for fractional porous medium and related equations (possibly involving stochastic perturbation).
The main focus is on the existence, uniqueness, and stability of the solutions of these equations, as well as on their efficient numerical approximation.
Keywords
• time-fractional porous medium and related equations
• subdiffusion processes
• memory effects
• stochastic perturbation
• numerical approximation
Organizers:
Prof. Dr. Petra Wittbold Important Dates: Deadline for manuscript submissions: 15 September 2025. All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/529HLR42LJ. =========================================================================== Books －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Boundary Value Problems Advanced Fractional Dynamic Equations on Time Scales ( Authors: Svetlin Georgiev) Details: https://doi.org/10.1007/978-3-031-94256-3 Book Description: This new edition presents an updated and expanded exploration of boundary value problems for fractional dynamic equations on arbitrary time scales, including Caputo fractional dynamic equations, impulsive Caputo fractional dynamic equations, and impulsive Riemann-Liouville fractional dynamic equations. In a new chapter, the author introduces time scale calculus and fractional time scale calculus. The book also covers initial value problems, boundary value problems, initial boundary value problems for each type of equation. The author provides integral representations of the solutions and proves the existence and uniqueness of the solutions. This second edition includes new and updated examples and problems. Author Biography: Sorbonne University, Paris, France Contents: ======================================================================== Journals －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Fractional Calculus and Applied Analysis (Volume 28, Issue 4) Gaofeng Zong Applied Mathematical Modelling (Selected) ======================================================================== Paper Highlight Dynamics of fractional stochastic diffusive SIRS epidemic model with Lévy noise Zaitang Huang, Yumei Lu, Qi Li, Yousu Huang Publication information: Chaos, Solitons & Fractals, Volume 200, November 2025. https://doi.org/10.1016/j.chaos.2025.116886 Abstract Owing to the fractional diffusion described by a spectral fractional Neumann Laplacian, the nonlocal diffusion model can be used to address the spatiotemporal dynamics driven by the nonlocal dispersal. In this paper, we mainly concerned with spatiotemporal dynamics in fractional stochastic diffusive SIRS epidemic model with Levy noise. We first state the well-posedness of the problem via iterative approximations and energy estimates. Then, the existence and uniqueness of random attractors and invariant measures for the equations are established. Finally, a large deviation principle result for solutions of fractional stochastic diffusive SIRS epidemic model with Levy noise is obtained by the method of weak convergence. Interestingly, this shows the effect of fractional Laplacians which can stabilize or destabilize the system which is significantly different from the classical Laplace operators. Numerical results show the effectiveness and advantage of our methods. Keywords Stochastic diffusive SIRS epidemic model; Fractional laplace operators; Random attractor; Invariant measure; Large deviation result －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Binghang Lu, ZhaoPeng Hao, Christian Moya, Guang Lin Publication information: Journal of Computational Physics, Volume 538, 1 October 2025. Abstract In this paper, we develop a physics-informed deep operator learning framework for solving multi-term time-fractional mixed diffusion-wave equations (TFMDwEs). We begin by deriving an L2 approximation, which achieves first-order accuracy for the Caputo fractional derivative of order β ∈ (1,2). Building upon this foundation, we propose the fPINN-DeepONet framework, a novel approach that integrates operator learning with the L2 approximation to efficiently solve fractional partial differential equations (FPDEs). Our framework is successfully applied to both fixed and variable fractional-order PDEs, demonstrating the framework's versatility and broad applicability. To evaluate the performance of the proposed model, we conduct a series of numerical experiments that involve dynamically varying fractional orders in both space and time, as well as scenarios with noisy data. These results highlight the accuracy, robustness, and efficiency of the fPINN-DeepONet framework. Keywords L2 Approximation; Operator learning; Machine learning; Data-driven scientific computing ========================================================================== The End of This Issue ∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽
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.
Elements of the Time Scale Calculus and Fractional Time Scale Calculus
Impulsive Riemann-Liouville Fractional Dynamic Equations
Boundary Value Problems for Caputo Fractional Dynamic Equations
Impulsive Caputo Fractional Dynamic Equations
Back Matter
Generalized fractional operators do not preserve periodicity
Roberto Garrappa, Katarzyna Górska, etc.
The fractional Sturm-Liouville problem with the Caputo derivative may lose the principal eigenvalue
Temirkhan S. Aleroev, Yulong Li
Dynamics of the Caputo fractional derivative
Marina Murillo-Arcila, Alfred Peris, Álvaro Vargas-Moreno
Controllability of Hilfer fractional backward evolution systems
Shouguo Zhu
Decay of mass for a semilinear heat equation with mixed local-nonlocal operators
Mokhtar Kirane, Ahmad Z. Fino, Alaa Ayoub
Solvability for a class of two-term nonlinear functional boundary value problems and its applications
Bingzhi Sun, Shuqin Zhang, Dongyu Yang
Multiplicity of couple solution for a fractional \((\varphi , \psi )\)-like system
Abderrahmane Lakhdari, Chaima Nefzi
Mixed local and nonlocal eigenvalue problems in the exterior domain
R. Lakshmi, Sekhar Ghosh
Stability analysis of Hilfer fractional stochastic switched dynamical systems with non-Gaussian process and impulsive effects
Rajesh Dhayal, Quanxin Zhu
Exponential sampling type neural network Kantorovich operators based on Hadamard fractional integral
Purshottam N. Agrawal, Behar Baxhaku
On the three dimensional generalized Navier-Stokes equations with damping
Nguyen ThiLe, LeTran Tinh
Approximate solutions for fractional stochastic integro-differential equation with short memory driven by non-instantaneous impulses
Surendra Kumar, Paras Sharma
Renormalized solutions for a non-local evolution equation with variable exponent
Le Xuan Truong, Nguyen Thanh Long, etc.
Fractional Bernoulli-Picard Iteration: A Powerful Tool for Solving Time-Fractional Partial Differential Equations
Soheyla Ansari, Mohammad Hossein Akrami
A computationally efficient numerical scheme for the solution of fourth-order time fractional partial integro-differential equation
Mukesh Kumar Rawani, Amit K. Verma
Adaptive finite-time fuzzy composite control for nonlinear fractional-order systems based on complexity avoidance
Xiaoyang Gao, Siwen Liu, etc.
Time-space fractional stochastic Ginzburg-Landau equations: Global solvability, Sobolev-Hölder regularity, and Talagrand’s transportation inequality
A modified Nishihara model with nonlinear time-varying viscosity via ψ-Caputo fractional derivative for salt rock
Li Ma, Yan Xu
A novel fractional grey forecasting model for high-tech industry growth trends
Sandang Guo, Jing Jia, etc.
Fractional-order viscoelastic model for tendons with multilevel self-similar structures
Xin Wang, Jianqiao Guo
Physics-informed neural fractional differential equations
Madasamy Vellappandi, Sangmoon Lee
Determining flux terms in a time fractional model
Mohamed BenSalah, Salih Tatar, etc.
Neural fractional differential equations
C. Coelho, M. Fernanda P. Costa, L. L. Ferrás
Optimal control of stochastic fractional rumor propagation model in activity-driven networks
Haojie Hou, Youguo Wang, etc.
Analytical solution of shallow arbitrarily shaped tunnels in fractional viscoelastic transversely isotropic strata
Zhi Yong Ai, Lei Yang, etc.
Multivariate grey prediction model with fractional time-lag parameter and its application
Bo Zeng, Yibo Tuo
Time-dependent deformation analyses of existing tunnels due to curved foundation pit excavation applying fractional derivative Merchant model and irregular Timoshenko beam
Zhiguo Zhang, Jian Wei, etc.
Seismic response analysis of a seawater–stratified seabed–bedrock system based on a fractional derivative viscoelastic model
Sen Zheng, Weihua Li, etc.
Neuro-enhanced fractional hysteresis modeling and identification by modified Newton-Raphson optimizer
Yuanyuan Li, Lei Ni, etc.
Modeling and analysis of a flexible spinning Euler-Bernoulli beam with centrifugal stiffening and softening: A linear fractional representation approach with application to spinning spacecraft
R. Rodrigues, D. Alazard, etc.
A novel approach for fractional pharmacokinetics modeling and integrating stochastic simulation techniques using Sibuya distribution
Yuhui Chen
Vibration suppression of a platform by a fractional type electromagnetic damper and inerter-based nonlinear energy sink
Nikola Nešić, Danilo Karličić, etc.
FPINN-deeponet: A physics-informed operator learning framework for multi-term time-fractional mixed diffusion-wave equations
https://doi.org/10.1016/j.jcp.2025.114184
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