FDA Express    Vol. 55, No. 3, Jun. 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 55_No 3_2025.pdf

　

◆  Latest SCI Journal Papers on FDA

(Searched Jun. 30, 2025)

　

◆  Call for Papers

Recent Developments in Multidimensional Fractional Differential Equations and Fractional Difference Equations

Advances in Fractional Differential Operators and Their Applications, 2nd Edition

 

◆  Books

Control of Singular Fractional Order Systems: LMI Approach

　

◆  Journals

Communications in Nonlinear Science and Numerical Simulation

Fractional Calculus and Applied Analysis

　

◆  Paper Highlight

Numerical analysis of blood flow and heat transfer in a stenosed and aneurysmal artery using a spatial fractional derivative constitutive model

On a Gronwall-type inequality for the general fractional integrals with the Sonin kernels and its applications

　

◆  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 Jun. 30, 2025)

 On positive solutions of certain singular fractional differential equations in orthogonal metric spaces

Eljaneid, NHE
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Volume:33 Published: Dec 2025

 Hyers-Ulam stability of fractional hybrid differential equation in Hölder space

Bhujel, M; Hazarika, B; etc.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Volume:33 Published: Dec 2025

 A Tikhonov-type method for inverse source problems for time-space fractional parabolic equations

Duc, NV and Nguyen, TP
APPLIED MATHEMATICS AND COMPUTATION Volume:507 Published: Dec 2025

 Representation of solution for fractional damped heat and wave equation on an infinite lattice via subordination techniques and Banach algebras

González-Camus, J
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume:552 Published: Dec 2025

 Novel application of q-HAGTM to analyze Hilfer fractional differential equations in diabetic dynamics

Kumawat, S; Bhatter, S; etc.
MATHEMATICS AND COMPUTERS IN SIMULATION Volume:238 Published: Dec 2025

 Hadamard fractional derivatives for a system of coupled implicit fractional pantograph differential equations

Palani, P; Prabu, D and Sivasundaram, S
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS Volume: 86 Published: Dec 2025

 Analysis and discretization of nonlinear generalized fractional stochastic differential equations

Ma, J; Guo, X; etc.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 150 Published: Nov 2025

  Averaging principle for a class of distribution dependent slow-fast stochastic differential equations driven by fractional Brownian motion and standard Brownian motion

Liu, ST
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 550 Published: Oct 2025

 SEQUENTIAL FRACTIONAL DIFFERENTIAL EQUATIONS WITH PARAMETRIC TYPE ANTI-PERIODIC BOUNDARY CONDITIONS

Ahmad, B; Ntouyas, SK; etc.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION Volume: 15 Published: Oct 2025

 THE EXISTENCE OF GLOBAL ATTRACTIVE SOLUTIONS FOR A CLASS OF TEMPERED FRACTIONAL DIFFUSION EQUATIONS

Zhang, SY
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION Volume:15 Published: Oct 2025

 EXISTENCE AND HYERS-ULAM STABILITY FOR BOUNDARY VALUE PROBLEMS OF TWO-TERM FRACTIONAL DIFFERENTIAL EQUATIONS WITH κ-CAPUTO DERIVATIVE

Xu, XP; Shen, Z; etc.
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION Volume: 15 Published: Oct 2025

 A NEW ITERATION ALGORITHM WITH RELAXATION FACTOR FOR THE CAUCHY PROBLEM OF TIME-FRACTIONAL DIFFUSION EQUATION

Li, ZP and Xiong, XT
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION Volume: 15 Published: Oct 2025

 UNIFORM LARGE DEVIATION PRINCIPLES OF FRACTIONAL STOCHASTIC P-LAPLACIAN REACTION-DIFFUSION EQUATIONS ON UNBOUNDED DOMAINS

Li, MD and Chen, PY
JOURNAL OF APPLIED ANALYSIS AND COMPUTATION Volume: 15 Published: Oct 2025

 Euler-Maruyama scheme for delay-type stochastic McKean-Vlasov equations driven by fractional Brownian motion

Gao, SB; Guo, Q; etc.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 149 Published: Oct 2025

 Fast numerical study on spatial nonuniform grids for two-dimensional fractional coupled equations with fractional Neumann boundary conditions

Kang, JX; Fan, WP and Lu, ZH
APPLIED MATHEMATICS LETTERS Volume: 169 Published: Oct 2025

 Using Lagrangian descriptors to reveal the phase space structure of dynamical systems described by fractional differential equations: Application to the Duffing oscillator

Theron, D; Susanto, H; etc.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 149 Published: Oct 2025

 Well posedness and general decay for a wave equation with logarithmic source term and distributed delay of fractional type

Choucha, A; Boulaaras, S and Rouhani, BD
JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS Volume: 16 Published: Sep 2025

 An operator method for composite fractional partial differential equations

Wang, HW and Li, F
CHAOS SOLITONS & FRACTALS Volume: 198 Published: Sep 2025

 Renormalized and entropy solutions for the fractional 1-Laplacian parabolic equation

Li, DD; Li, Y and Zhang, C
JOURNAL OF EVOLUTION EQUATIONS Volume: 25 Published: Sep 2025

　

　

　

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Call for Papers

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Recent Developments in Multidimensional Fractional Differential Equations and Fractional Difference Equations

( A special issue of Fractal and Fractional )

Dear Colleagues,
The theory of abstract fractional differential equations is an active field of research for many authors. Fractional calculus and fractional differential equations, which have emerged as the most important field of applied mathematics in the last century, can be viewed as a special aspect of this theory.
On the other hand, fractional calculus and fractional differential equations have received significant attention in recent years. Muti-dimensional fractional calculus is fundamentally important in the modeling of various phenomena concerning complex dynamic systems, frequency response analysis, image processing, interval–valued systems and neural networks.
The main aim of this Special Issue is to present recent developments in the theory and application of fractional calculus, fractional integro–differential-difference equations and multidimensional fractional calculus. We strongly encourage the submission of papers concerning fractional partial differential–difference equations that depend on several variables.

Keywords:

- Fractional calculus
- Fractional differential equations
- Fractional difference equations
- Multidimensional fractional calculus
- Multidimensional fractional differential equations
- Multidimensional partial fractional differential equations
- Theory and applications

Organizers:

Prof. Dr. Marko Kostić
Prof. Dr. Wei-Shih Du

Important Dates:

Deadline for conference receipts: 18 July 2025.

All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/NUMQ049W57.

Advances in Fractional Differential Operators and Their Applications, 2nd Edition

( A special issue of Fractal and Fractional )

Dear Colleagues,
This Special Issue, published by MDPI, is dedicated to the theory and practice of fractional differential operators and corresponding equations. Although the field of fractional derivatives is, in general, relatively old, there remain numerous unsolved problems and wide scope for further research. Thus, we welcome the submission of papers in the area of hybrid fractional equations (e.g., mixed Riemann–Liouville/Caputo derivatives and other combinations of such derivatives). The scope of this Special Issue includes, but is not limited to, the following topics:

• Generalized and fractional derivatives and integrals;
• Riemann–Liouville derivatives and integrals;
• Caputo derivatives and integrals;
• Spectral and asymptotic theory;
• Qualitative theory;
• Variational principles;
• Applications of fractional derivatives to any area of science or the humanities.

Organizers:

Prof. Dr. Angelo B. Mingarelli
Dr. Leila Gholizadeh Zivlaei
Dr. Mohammad Dehghan

Important Dates:

Deadline for manuscript submissions: 25 July 2025.

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

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Books

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Control of Singular Fractional Order Systems: LMI Approach

( Authors: Saliha Marir , Mohammed Chadli )

Details: https://doi.org/10.1007/978-3-031-87382-9

Book Description:

This book provides a comprehensive study of singular fractional-order systems, presenting a novel perspective on their analysis and control. Using the Linear Matrix Inequalities approach, it provides conditions for admissibility, robust admissibility, stabilization, and robust stabilization of fractional singular linear time-invariant systems. The methods discussed address key challenges in stability and robustness, and provide innovative solutions to open problems in fractional-order control theory.
Aimed at control scientists, graduate students, and advanced undergraduates, this work bridges theoretical developments and practical applications, making it a valuable resource for understanding and advancing the field of fractional-order systems. It is particularly suitable for those seeking new directions in control systems research or who wish to apply fractional tools to dynamic systems modeling and control.
With its unique focus and broad scope, this book serves as an indispensable reference for courses such as "Analysis and Control of Fractional-Order Systems" and "LMI-Based Control of Singular Fractional-Order Systems".

Author Biography:

University of Science and Technology, Mohamed Boudiaf, Bir El Djir, Oran, Algeria
University Paris-Saclay Evry, IBISC Laboratory, Évry, France

Contents:

Front Matter

Overview on Fractional Calculus

Stability Analysis of Fractional-Order Systems

Stabilization of Fractional-Order Systems

H∞ Control for Fractional-Order Systems

Admissibility Analysis of Singular Fractional-Order Systems

Stabilization of Singular Fractional-Order Systems

H∞ Control for Singular Fractional-Order Systems

Back Matter

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 Journals

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Communications in Nonlinear Science and Numerical Simulation

 (Selected)

  An innovative hybrid model coupling non-local fractional PDEs and bilateral convolution for denoising degraded digital images

S. Kassimi, H. Moussa, H. Sabiki

  A novel criterion on finite-time stability of fractional-order impulsive time-delay Hopfield neural networks

Wenbo Wang, Feifei Du salah

  Long-time diffusion behavior of variable-coefficient fractional reaction–diffusion modeling pattern dynamics

Che Han, Xing Lü, Hao Tian

  Finite-time contractive stability for fractional-order impulsive systems with time delays

P. Gokul, Salem Ben Said

  (Non)Commutativity and associativity of general fractional derivatives with different Sonin kernels

Vasily E. Tarasov

 Application of a reflected forward backward splitting method with momentum to a fractional-order lung cancer model

Chinedu Izuchukwu, David Amilo, etc.

 Fully decoupled fractional-step methods for non-linear viscoelastic flows: Natural heat convection, viscous dissipation and phase change

Ismael Aguirre, Douglas R. Q. Pacheco, Ernesto Castillo

  Application of fractional derivatives in modeling the heat flow in the thermal protection system

Rafał Brociek, Edyta Hetmaniok, Damian Słota

  Analysis and discretization of nonlinear generalized fractional stochastic differential equations

Jie Ma, Xu Guo, etc.

  On a Gronwall-type inequality for the general fractional integrals with the Sonin kernels and its applications

Mohammed Al-Refai, Mohammadkheer Al-Jararha, Yuri Luchko

  Fractional order induced bifurcations in Caputo-type denatured Morris–Lecar neurons

Indranil Ghosh, Hammed Olawale Fatoyinbo

  Hamilton–Pfaff type PDEs through multi-dimensional fractional optimization problems

Octavian Postavaru, Antonela Toma, Savin Treanţă

  Hidden memory chaotic attractors in simple nonequilibrium fractional order systems

Bichitra Kumar Lenka, Ranjit Kumar Upadhyay

  Koopman prediction for high-dimensional fractional-order chaotic system with uncertainties

Li Zhang

  Exponential stability of fractional order impulsive switched system with stable and unstable subsystems

Mariam Al Qinqin Liao, Danfeng Luo

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Fractional Calculus and Applied Analysis

  (Volume 28, Issue 3)

　

  Para-Markov chains and related non-local equations

Lorenzo Facciaroni, Costantino Ricciuti, etc.

  On solutions of fractional nonlinear Fokker-Planck equation

Komal Singla, Nikolai Leonenko

  Fractional diffusion in the full space: decay and regularity

Markus Faustmann, Alexander Rieder

  Existence, nonexistence and multiplicity of bounded solutions to a nonlinear BVP associated to the fractional Laplacian

JoséJosé Carmona Tapia, Rubén Fiñana Aránega

  No-regret and low-regret controls of space-time fractional parabolic Sturm-Liouville equations in a star graph

Gisèle Mophou, Maryse Moutamal, Mahamadi Warma

  An anomalous fractional diffusion operator

Xiangcheng Zheng, V. J. Ervin, Hong Wang

  Ground states for p-fractional Choquard-type equations with doubly or triply critical nonlinearity

Masaki Sakuma

  Fractional differential equations involving Erdélyi–Kober derivatives with variable coefficients

Fatma Al-Musalhi, Arran Fernandez

  The oscillatory solutions of multi-order fractional differential equations

Ha Duc Thai, Hoang The Tuan

  Inverse coefficient problems for the heat equation with fractional Laplacian

Azizbek Mamanazarov, Durvudkhan Suragan

  Inverse source problems for time-fractional nonlinear pseudoparabolic equations with p-Laplacian

Khonatbek Khompysh, Michael Ruzhansky

  Discrete fractional-order Halanay inequality with mixed time delays and applications in discrete fractional-order neural network systems

Xiang Liu, Yongguang Yu

  On the multivariate generalized counting process and its time-changed variants

Kuldeep Kumar Kataria, Manisha Dhillon

  The nonlinear fractional Rayleigh-Stokes problem on an infinite interval

Jing Na Wang

  Ground state solution for a generalized Choquard Schrdinger equation with vanishing potential in homogeneous fractional Musielak Sobolev spaces

Shilpa Gupta, Gaurav Dwivedi

  Mild solutions to the Cauchy problem for time-space fractional Keller-Segel-Navier-Stokes system

Ziwen Jiang & Lizhen Wang

  Multiple solutions for nonsmooth fractional Hamiltonian systems

Mohsen Timoumi

  Pseudo-differential operators with forbidden symbols on Triebel–Lizorkin spaces

Xiaofeng Ye, Xiangrong Zhu

  Invariant tori for the fractional nonlinear Schrödinger equation with nonlinearity periodically depending on spatial variable

Jieyu Liu, Jing Zhang

  Harnack inequalities for functional SDEs driven by fractional Ornstein-Uhlenbeck process

Zhi Li, Meiqian Liu, Liping Xu

  Fractional Musielak-Sobolev spaces: study of generalized double phase problem with Choquard-logarithmic nonlinearity

Hamza El-houari, Hicham Moussa, Hajar Sabiki

  Stochastic heat equation driven by space-only fractional Lévy noise

Lamine Salem, Mounir Zili

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 Paper Highlight

Numerical analysis of blood flow and heat transfer in a stenosed and aneurysmal artery using a spatial fractional derivative constitutive model

Yuehua Jiang, Yong Zhang, Hongguang Sun

Publication information: Physics of Fluids, Volume 37, 10 June 2025.

https://doi.org/10.1063/5.0270978

Abstract

Hemodynamics factors influenced by blood flow significantly affect aneurysms growth and rupture. While most studies focus on the temporal effects of blood flow, the potential impact of non-local spatial effects is often overlooked. However, previous research suggests that jet flow from proximal stenosis can lead to long-range (non-local) redistribution of wall shear stress at aneurysm initiation sites. This study employs a non-local spatial fractional derivative non-Newtonian fluid model to characterize the pseudoplastic behavior of blood and analyze flow in stenosis and aneurysmal arteries. Results show that the fractional derivative order (non-local parameter) can serve as an index to characterize cholesterol-rich blood in clinical diagnostics. Strong shear-thinning property of blood characterized by higher-order fractional derivative model reduces viscosity under high shear rates, leading to accelerated blood flow and increased wall shear stress. Subsequently, the increasement of wall shear stress gradient in regions of vascular stenosis and aneurysms, potentially raises the risk of aneurysm rupture in degenerated aneurysm walls.

Topics

Heat transfer, Spatial effect, Fractional calculus, Nanoparticle, Non Newtonian fluids, Constitutive relations, Haemodynamics, Boundary layer flow, Cholesterol, Cardiovascular system

　

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On a Gronwall-type inequality for the general fractional integrals with the Sonin kernels and its applications

  Mohammed Al-Refai, Mohammadkheer Al-Jararha, Yuri Luchko

Publication information: Communications in Nonlinear Science and Numerical Simulation, Volume 150, 10 June 2025.
https://doi.org/10.1016/j.cnsns.2025.108985

Abstract

In this paper, for the first time, we formulate and prove a Gronwall-type inequality for the general fractional integrals with the Sonin kernels and with variable coefficients. Most of the Gronwall-type inequalities for the Fractional Calculus operators introduced in the literature so far are particular cases of this inequality. In the second part of the paper, the Gronwall-type inequality for the general fractional integrals with the Sonin kernels is applied for investigation of initial value problems for the non-linear fractional differential equations with the general fractional derivatives in the Riemann–Liouville sense and with the 1st level general fractional derivatives. This analysis covers the equations with both the Riemann–Liouville and Hilfer fractional derivatives and with several other types of fractional derivatives. In particular, we derive the uniqueness and continuous dependence of solutions to these problems on the initial data.

Highlights

• A new Gronwall-type inequality for general fractional integrals with Sonin kernels.
• Non-linear fractional differential equations with general fractional derivatives.
• Uniqueness and continuous dependence of their solutions on the initial data.
• Particular cases with the Riemann–Liouville and the Hilfer fractional derivatives.

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The End of This Issue

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