FDA Express    Vol. 55, No. 1, Apr. 30, 2025

All issues: http://jsstam.org.cn/fda/

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 55_No 1_2025.pdf

◆  Latest SCI Journal Papers on FDA

(Searched Apr. 30, 2025)

◆  Call for Papers

Recent Advances in Fractional-Order Neural Networks: Theory and Application, 2nd Edition

Fractional Order Systems Modelling and Control

◆  Books

Modeling of Discrete and Continuous Systems

◆  Journals

Applied Mathemaics Letters

Fractional Calculus and Applied Analysis

◆  Paper Highlight

Neural network approximation of the composition of fractional operators and its application to the fractional Euler-Bernoulli beam equation

Neuromorphic dynamics and behavior synchronization of fractional-order memristive synapses

◆  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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(Searched on Apr. 30, 2025)

 A robust numerical scheme and analysis for a class of multi-term time-fractional advection-diffusion equation with variable coefficients

Sabir, S; Ahmad, A; etc.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING Volume:71 Published: Apr 2025

 Fractional mean field equations: Theory and application on finite graphs

Liu, Y
JOURNAL OF DIFFERENTIAL EQUATIONS Volume:436 Published: Aug 2025

 Multiple and weak Markov properties in Hilbert spaces with applications to fractional stochastic evolution equations

Kirchner, K and Willems, J
STOCHASTIC PROCESSES AND THEIR APPLICATIONS Volume:186 Published: Aug 2025

 Fractional derivatives in advection-dispersion equations: A comparative study

Pandey, AK
JOURNAL OF HYDROLOGY Volume:657 Published: Aug 2025

 Abundant exact solutions of the fractional (3+1)-dimensional Yu-Toda-Sasa-Fukuyama (YTSF) Equation using the Bell Polynomial-based neural network method

Zhu, Y; Li, KH; etc.
CHAOS SOLITONS & FRACTALS Volume:196 Published: Jul 2025

 Iterative weighted Tikhonov regularization technique for inverse problems in time-fractional diffusion-wave equations within cylindrical domains

KLong, LD; Moghaddam, BP and Gurefe, Y
COMPUTATIONAL & APPLIED MATHEMATICS Volume: 44 Published: Jul 2025

  Efficient families of higher-order Caputo-type numerical schemes for solving fractional order differential equations

Shams, M and Carpentieri, B
ALEXANDRIA ENGINEERING JOURNAL Volume: 124 Published: Jun 2025

  Discrete Laplace transform for interval-valued functions and its applications to interval fractional difference equations

Liu, XL; Ye, GJ and Liu, W
FUZZY SETS AND SYSTEMS Volume: 509 Published: Jun 2025

 Constraint minimizers of mass critical fractional Kirchhoff equations: concentration and uniqueness

Liu, LT; Radulescu, VD and Yuan, S
NONLINEARITY Volume: 38 Published: Apr 2025

 Numerical computation of fractional Kawahara and modified Kawahara equations in Caputo sense on integral transforms

Sahu, I and Jena, SR
JOURNAL OF SUPERCOMPUTING Volume:81 Published: Apr 2025

 High performance adaptive step size fractional numerical scheme for solving fractional differential equations

Shams, Mudassir and Alalyani, Ahmad
Scientific reports Volume: 15 Published: Apr 2025

 Soliton solutions of the time-fractional nonlinear Schrödinger equation with refractive index and generalized nonlocal nonlinearity via two integration methods

Mahmood, SS and Murad, MAS
MODERN PHYSICS LETTERS B Published: Apr 2025 (Early Access)

 A q-homotopy analysis transformation method for solving (2+1)-dimensional coupled fractional nonlinear Schrödinger equations

Wang, PP; Feng, XF and He, SQ
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS Published: Apr 2025 (Early Access)

 Studies on Fractional Differential Equations With Functional Boundary Condition by Inverse Operators

Li, CK
MATHEMATICAL METHODS IN THE APPLIED SCIENCES Published: Apr 2025 (Early Access)

 Stability analysis of hybrid langevin equation via two fractional operators

Almaghamsi, L
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY Published: Apr 2025 (Early Access)

 Ulam stability for nonlinear boundary value problems for impulsive Caputo type fractional delay differential equations

Agarwal, RP; Hristova, S and O'Regan, D
BOUNDARY VALUE PROBLEMS Volume: 2025（1） Published: Apr 2025

 Operator-Based Approach for the Construction of Solutions to (CD(1/n))k-Type Fractional-Order Differential Equations

Telksniene, I; Navickas, Z; etc.
MATHEMATICS Volume: 13 Published: Apr 2025

  Fractional sub-equation neural networks (fSENNs) method for exact solutions of space-time fractional partial differential equations.

Wang, Jiawei; Liu, Yanqin; etc.
Chaos (Woodbury, N.Y.) Volume: 61 Published: Apr 2025

 A deep learning framework for solving fractional partial differential equations

Ali, A; Senu, N; etc.
PHYSICA SCRIPTA Volume: 100 Published: Apr 2025

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Call for Papers

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Recent Advances in Fractional-Order Neural Networks: Theory and Application, 2nd Edition

( A special issue of Fractal and Fractional )

Dear Colleagues,
The field of fractional-order neural networks refers to research that incorporates the concepts of fractional calculus into the related theory and application of neural networks. It is introduced to accurately describe the physical process and system state with heredity and memorability. With the in-depth study of fractional-order neural network models and dynamics analysis (e.g., stability, synchronization, bifurcation, etc.), more control methods and control techniques are applied to these systems, which will enrich the theoretical system of fractional-order neural networks. Additionally, fractional-order neural networks have infinite memory properties, which can further improve the design, characterization, and control capabilities of network models for many practical problems. These concepts have great application prospects and research value in biological nervous systems, circuit design and simulation, artificial intelligence, and other fields.
The focus of this Special Issue is to continue to advance research on topics relating to the theory, control, design, and application of fractional-order neural networks. Topics that are invited for submission include (but are not limited to):

- Fractional-order neural network model;
- Dynamic analysis and control of fractional-order neural networks;
- Circuit design and simulation of fractional-order neural networks;
- Applications of fractional-order neural networks for biology and biomedicine;
- Applications of fractional-order circuit models for artificial intelligence.

Keywords:

- Fractional calculus
- Dynamics analysis
- Biological nervous system
- Circuit design and simulation
- Artificial intelligence

Organizers:

Prof. Dr. Zhouchao Wei
Dr. Lulu Lu

Important Dates:

Deadline for conference receipts: 25 May 2025 | .

All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/E8RI1S1F6M.

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 manuscript submissions: 30 Dec 2025 .

All details on this conference are now available at: https://link.springer.com/collections/hehbfeafih.

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( Authors: Mohamed Kharrat, Nouressadat Touafek, Moez Krichen )

Details: https://doi.org/10.1007/978-981-97-8715-9

This book contains a comprehensive collection of chapters on recent and original research, along with review articles, on mathematical modeling of dynamical systems described by various types of differential equations. Structured into 18 chapters dedicated to exploring different aspects of differential equations and their applications in modeling both discrete and continuous systems, it highlights theoretical advancements in mathematics and their practical applications in modeling dynamic systems. Readers will find contributions by renowned scholars who delve into the intricacies of nonlinear dynamics, stochastic processes, and partial differential equations. This book is an essential resource for researchers, academicians, and practitioners in the field of mathematical modeling.

Author Biography:

Department of Mathematics, Jouf University, Sakakah, Saudi Arabia
Department of Mathematics, University of Jijel, Jijel, Algeria
Department of Information Technology, Al-Baha University, Alaqiq, Saudi Arabia

Contents:

Front Matter

Fractional Differential Equations in Engineering and for Polyurethane Foam Modelling

A New Operator Approach for Solving Time-Fractional Nonlinear Burgess Equation

Explicit Form for the Solutions of a System of Difference Equations

Stochastic Integrodifferential Equations with Deviating Argument Driven by Poisson Jumps: Optimal Controls

A Review on Fractional Calculus in Modeling of Cancer

Conformable Fractional Taylor Series Algorithm for Solving Temporal Fractional Reaction–Diffusion–Convection Equation

Modified Some n-Point Fractional Formulae with Richardson Extrapolation

Analysis of Alzheimer’s Disease Using Nonlocal Operator

A Stable Relaxation Approach for Valuing European Options Across Diverse Time-Fractional Models

Certain Generalization of Appell’s Functions and Riemann–Liouville Fractional Derivative Operator and Their Applications

A Study of Integral Transforms Associated with Srivastava–Daoust Multivariable Hypergeometric Functions

A Measure Second-Order Maximal Monotone Differential Inclusion

Certain Integrals Involving Generalized Laguerre Polynomials and Bessel Function and Their Application

Nonlinear Dynamical Systems in a Nutshell

Sasaki Gradient Tensor and Para-Complex Structures

New Several Types of Difference Equations for Degenerate Quantum Bernoulli Polynomials Using (q, h)-Derivative

Optimal Control Problems Governed by a Class Nonlinear Dynamical System

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Fractional Calculus and Applied Analysis

  (Volume 28, Issue 2)

Mohammed Al-Refai, Yuri Luchko

  Strong stationarity for non-smooth control problems with fractional semi-linear elliptic equations in dimension N < 3

Cyrille Kenne, Gisèle Mophou, Mahamadi Warma

 Simple difference schemes for multidimensional fractional Laplacian and fractional gradient

Jaromír Kukal, Michal Beneš

  Infinitely many solutions for impulsive fractional Schrödinger-Kirchhoff-type equations involving p-Laplacian via variational method

Yi Wang, Lixin Tian

  Pullback dynamics of 2D non-autonomous Reissner-Mindlin-Timoshenko plate systems

Baowei Feng, Mirelson M. Freitas, etc.

  On positive solutions of fractional elliptic equations with oscillating nonlinearity

Francisco J. S. A. Corrêa, César E. T. Ledesma, Alânnio B. Nóbrega

  Cauchy problem for time-space fractional incompressible Navier-Stokes equations in R^n

Miao Yang, LiZhen Wang, LuSheng Wang

  ψ-Hilfer type linear fractional differential equations with variable coefficients

Fang Li, Huiwen Wang

 Topological properties of the solution set for Caputo fractional evolution inclusions involving delay

Huihui Yang, He Yang

  Space-time fractional parabolic equations on a metric star graph with spatial fractional derivative of Sturm-Liouville type: analysis and discretization

Vaibhav Mehandiratta, Mani Mehra

  On fractional differential inclusion with damping driven by variational-hemivariational inequality

Yunshui Liang, LuChuan Ceng, Shengda Zeng

 Investigation of controllability criteria for Caputo fractional dynamical systems with delays in both state and control

Anjapuli Panneer Selvam, Venkatesan Govindaraj

 Abstract multi-term fractional difference equations

Marko Kostić

 Differential transforms related to Caputo time-fractional derivatives and semigroups generated by fractional Schrödinger operators

Zhiyong Wang, Pengtao Li, Yu Liu

 On a uniqueness criterion for nonlinear fractional differential equations

Nguyen Minh Dien

 Existence of at least k solutions to a fractional p-Kirchhoff problem involving singularity and critical exponent

Sekhar Ghosh, Debajyoti Choudhuri, Alessio Fiscella

 Controllability of multi-term fractional-order impulsive dynamical systems with -Caputo fractional derivative

Md. Samshad Hussain Ansari, Muslim Malik

Publication information: Applied Mathematics and Computation, Volume 501, 15 September 2025.

https://doi.org/10.1016/j.amc.2025.129475

Abstract

In this paper, we propose a new approach to approximation of the left and the right fractional Riemann - Liouville integrals as well as the compositions of these two operators, based on a shallow neural network with ReLU as an activation function. We apply the proposed method to the fractional Euler - Bernoulli beam equation with fixed-supported and fixed-free ends, and we provide numerical simulations for constant, power and trigonometric functions. Finally, we compare the obtained results with the exact solutions of the considered problems.

Publication information: Chaos, Solitons and Fractals, Volume 197, 26 April 2025.
https://doi.org/10.1016/j.chaos.2025.116469

Abstract