FDA Express Vol. 54, No. 2
FDA Express Vol. 54, No. 2, Feb. 28, 2025
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Institute of Soft Matter Mechanics, Hohai University
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◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Analysis and Applications of Fractional Calculus and Mathematical Modelling
◆ Books Fractional Differential and Integral Operators with Respect to a Function ◆ Journals Fractional Calculus and Applied Analysis Applied Mathematical Modelling ◆ Paper Highlight
A regional spatial nonlocal continuous time random walk model for tracer transport in fluids
◆ Websites of Interest Fractal Derivative and Operators and Their Applications Fractional Calculus & Applied Analysis ======================================================================== Latest SCI Journal Papers on FDA －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Li, XH; Wong, PJY and Alikhanov, AA
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume:464 Published: Aug 2025
Zhu, XG and Zhang, YP
ALEXANDRIA ENGINEERING JOURNAL Volume: 117 Published: Apr 2025
Wang, ZY; Liu, JX; etc.
ENERGY Volume:316 Published: Feb 2025
Asymptotic analysis of solutions to fractional diffusion equations with the Hilfer derivative
Li, ZQ
COMPUTATIONAL & APPLIED MATHEMATICS Volume: 44 Published: Feb 2025
A fast parallel difference method for solving the time-fractional generalized fisher equation
Longtao Chai, Lifei Wu, Xiaozhong Yang
JOURNAL OF APPLIED ANALYSIS & COMPUTATION Volume: 15 Published: Jun 2025
Zhu, JX; Yu, L and Jie, H
COMPUTATIONAL & APPLIED MATHEMATICS Volume: 44 Published: Feb 2025
Wei, Q; Wang, W; etc.
PHYSICAL REVIEW E Volume: 111 Published: Jan 2025
Bozkurt, MA; Köse, Y and Çelik, S
ENERGY SOURCES PART B-ECONOMICS PLANNING AND POLICY Volume: 20 Published: Dec 2025
Generalized exponential time differencing for fractional oscillation models
Honain, AH; Furati, KM; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 461 Published: Jun 2025
Saha, S and Kayal, S
PHYSICA D-NONLINEAR PHENOMENA Volume:473 Published: Mar 2025
Sun, JK and Wang, JM
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 142 Published: Mar 2025
Al-Qurashi, M; Ramzan, S; etc.
AIN SHAMS ENGINEERING JOURNAL Volume: 16 Published: Feb 2025
Fractional Bateman equations in the Atangana-Baleanu sense
Jornet, M
PHYSICA SCRIPTA Volume: 100 Published: Feb 2025
Self-similar solutions for the fractional viscous Burgers equation in Marcinkiewicz spaces
de Oliveira, EC; Lima, MED and Viana, A
COMPUTATIONAL & APPLIED MATHEMATICS Volume: 44 Published: Feb 2025
Salah, EY; Sontakke, B; etc.
SCIENTIFIC REPORTS Volume: 15 Published: Jan 2025
Space-Time Fractional Bessel Diffusion Equation
Bouzeffour, F
JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS Volume: 32 Published: Jan 2025
Shah, RH and Irshad, N
INTERNATIONAL JOURNAL OF THEORETICAL PHYSICS Volume: 64 Published: Jan 2025
Durdiev, D and Rahmonov, A
FRACTIONAL CALCULUS AND APPLIED ANALYSIS Volume: 28 Published: Feb 2025
Nie, XB; Cao, BQ; etc.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS Volume: 55 Published: Mar 2025
========================================================================== Call for Papers －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－
Boundary Value Problems for Nonlinear Fractional Differential Equations: Theory, Methods and Application
( A special issue of Fractal and Fractional )
Dear Colleagues, This Special Issue is devoted to the broad research areas involving Boundary Value Problems (BVPs) of Nonlinear Fractional Differential Equations. The study of nonlinear BVPs for Ordinary Differential Equations (ODEs), Partial Differential Equations (PEDs), Fractional Differential Equations (FDEs), and their discrete counterparts in the form of Difference Equations has a long history and various applications in sciences, engineering, social activities, and natural phenomenon. In particular, BVPs for fractional-order differential equations have attracted more and more interest and have achieved significant improvements recently, partly due to their new applications in physics, control theory, quantitative finance, econometrics, and signal processing.
It is known that fractional-order equations have different behavior from the corresponding integer order equations. Although the traditional topological and numerical methods in dealing with differential equations are applicable to some fractional problems, new methods and techniques have been developed particularly for FDEs. For example, it has been shown that neural networks are efficient in solving and analyzing certain types of FDEs. Fractional techniques have also been applied to train deep learning neural networks to achieve better learning effect for artificial intelligence.
We are interested in the most recent advances in the theory, methods, and applications of FDEs. Topics include, but are not limited to:
- Existence and positivity of solutions;
- Uniqueness and multiplicity of solutions;
- Stability and equilibrium;
- Fixed point methods and applications;
- Modeling with FDEs;
- Numerical solutions;
- Neural networks and FDEs;
- Eigenvalue problems;
- Fractional q-differential equations.
Keywords:
- Existence and positivity of solutions
- Uniqueness and multiplicity of solutions
- Stability and equilibrium
- Fixed point methods and applications
- Modeling with FDEs
- Numerical solutions
- Neural networks and FDEs
- Eigenvalue problems
- Fractional q-differential equations
Organizers:
Prof. Dr. Wenying Feng
Important Dates:
Deadline for conference receipts: 31 March 2025.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/1478ZPH751.
Analysis and Applications of Fractional Calculus and Mathematical Modelling
( A special issue of Fractal and Fractional )
Dear Colleagues, Almost 330 years after Leibniz’s letter to L'Hopital, fractional calculus and derivatives of arbitrary order are still being used extensively and widely in both fundamental and applied research. Consequently, it is important to consider the following question: How far can knowledge and scientific boundaries be pushed with the aid of fractional calculus? This Special Issue, entitled “Analysis and Applications of Fractional Calculus and Mathematical Modelling”, intends to provide readers with state-of-the-art research publications showing ideas and challenges for future research and contribute to the beginning of collaboration and exchange among different research groups in fractional calculus worldwide in the future. To achieve this goal, the Special Issue has two major branches. In the first one, manuscripts with fundamental research involving analytical mathematical methods, novel derivative definitions, and numerical methods for faster solutions, among others, are very welcome. In the second branch, applied research studies and scenarios will certainly aid in the development of a milestone Special Issue by investigating fractional calculus' applications to different research areas and fields, such as process systems engineering, transport phenomena, biological systems, electrical circuits, and materials science, among others. From these two branches—fundamental and applied research—this Special Issue intends to become a valuable reference for both beginners and senior researchers in the academic world and also for practitioner professionals in industry.
Keywords:
- Fractional calculus
- Fractional differential and integral equations
- Fractional models
- Mathematical modelling
- Fractional dynamics
- Modeling simulation
- Process control
- Application of fractional calculus, focusing on modeling and optimization
Organizers:
Dr. Marcelo Kaminski Lenzi
Important Dates:
Deadline for manuscript submissions: 31 March 2025.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/G0BS0WA863.
=========================================================================== Books －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Fractional Differential and Integral Operators with Respect to a Function
( Authors: Abdon Atangana , İlknur Koca )
Details:https://doi.org/10.1007/978-981-97-9951-0 Book Description: This book explores the fundamental concepts of derivatives and integrals in calculus, extending their classical definitions to more advanced forms such as fractional derivatives and integrals. The derivative, which measures a function's rate of change, is paired with its counterpart, the integral, used for calculating areas and volumes. Together, they form the backbone of differential and integral equations, widely applied in science, technology, and engineering. However, discrepancies between mathematical models and experimental data led to the development of extended integral forms, such as the Riemann–Stieltjes integral and fractional integrals, which integrate functions with respect to another function or involve convolutions with kernels. These extensions also gave rise to new types of derivatives, leading to fractional derivatives and integrals with respect to another function. While there has been limited theoretical exploration in recent years, this book aims to bridge that gap. It provides a comprehensive theoretical framework covering inequalities, nonlinear ordinary differential equations, numerical approximations, and their applications. Additionally, the book delves into the existence and uniqueness of solutions for nonlinear ordinary differential equations involving these advanced derivatives, as well as the development of numerical techniques for solving them.
Author Biography:
Abdon Atangana, University of the Free State, Bloemfontein, South Africa
İlknur Koca, Muğla Sıtkı Koçman University, Fethiye, Türkiye
Contents:
Front Matter
History of Differential and Integral Calculus
Derivative with Respect to a Function: Derivatives, Definitions, and Properties
Integral Operators, Definitions, and Properties
Inequalities Related to Global Fractional Derivatives
Inequalities Associated to Integrals
Existence and Uniqueness of IVP with Global Differentiation on via Picard Iteration
Existence and Uniqueness via Carathéodory Approach
Existence and Uniqueness Analysis of Nonlocal Global Differential Equations with Expectation Approach
Chaplygin’s Method for Global Differential Equations
Numerical Analysis of IVP with Classical Global Derivative
Numerical Analysis of IVP with Riemann–Liouville Global Derivative
Numerical Analysis of IVP with Caputo–Fabrizio Global Derivative
Numerical Analysis of IVP with Atangana–Baleanu Global Derivative
Examples and Applications of Global Fractional Differential Equations
Back Matter
======================================================================== Journals －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Fractional Calculus and Applied Analysis (Volume 28, Issue 1) Rafał Kamocki, Cezary Obczyński Mark Edelman Marian Slodička Tian Feng, YangQuan Chen Dariusz Idczak Durdimurod Durdiev, Askar Rahmonov Kee Qiu, Michal Fečkan, JinRong Wang Shitao Liu Mustapha Benoudi, Rachid Larhrissi Fei Gao, Liujie Guo, etc. Cornelia Mihaila, Brian Seguin Eudes M. Barboza, Olímpio H. Miyagaki, etc. Wen-Shuo Yuan, Bin Ge, etc. Anis Riahi, Luigi Accardi, etc. Chenkuan Li Lijuan Zhang, Yejuan Wang Jorge González-Camus Jianfei Huang, Junlan Lv, Sadia Arshad Liangliang Sun, Zhaoqi Zhang, Yunxin Wang Applied Mathematical Modelling (Selected) Haojie Hou, Youguo Wang, etc. Zhi Yong Ai, Lei Yang, etc. Bo Zeng, Yibo Tuo Zhiguo Zhang, Jian Wei, etc. Sen Zheng, Weihua Li, etc. Yuanyuan Li, Lei Ni ,etc. R. Rodrigues, D. Alazard, etc. Yuhui Chen Nikola Nešić, Danilo Karličić, etc. Zhenxiu Cao, Xiangyan Zeng, Fangli He Shaojiu Bi, Minmin Li, Guangcheng Cai Ke Ren, Jin Zhang, etc. Xue-Yang Zhang, Zhen-Liang Hu, etc. S. M. Cai, Y. M. Chen, Q. X. Liu Minmin Li, Shaojiu Bi, Guangcheng Cai ======================================================================== Paper Highlight A regional spatial nonlocal continuous time random walk model for tracer transport in fluids ZhiPeng Li, HongGuang Sun
Asymptotic cycles in fractional generalizations of multidimensional maps
A collection of correct fractional calculus for discontinuous functions
A time-space fractional parabolic type problem: weak, strong and classical solutions
Existence and approximate controllability of Hilfer fractional impulsive evolution equations
Mixed slow-fast stochastic differential equations: Averaging principle result
Spatial β-fractional output stabilization of bilinear systems with a time α-fractional-order
Hardy–Hénon fractional equation with nonlinearities involving exponential critical growth
Study on the diffusion fractional m-Laplacian with singular potential term
Appell system associated with the infinite dimensional Fractional Pascal measure
Continuity of solutions for tempered fractional general diffusion equations driven by TFBM
The quasi-reversibility method for recovering a source in a fractional evolution equation
Optimal control of stochastic fractional rumor propagation model in activity-driven networks
Multivariate grey prediction model with fractional time-lag parameter and its application
Publication information: Physics of Fluids, Volume 37, 7 Feburary 2025.
https://doi.org/10.1063/5.0249919 Abstract Geological formations exhibit complex and diverse structures, which affect the transport behavior of tracers such as contaminants and sediments in fluids through various complex processes. Traditional models like the advection–diffusion equation and continuous time random walk (CTRW) have limitations in characterizing regional spatial nonlocal tracer transport processes, leading to unpredictable results. This study proposes a novel regional spatial–temporal (ST) nonlocal CTRW (ST-CTRW) model that employs the peridynamic differential operator and memory kernel to incorporate spatial–temporal nonlocalities. The ST-CTRW model can effectively capture both spatial and temporal nonlocal transport behaviors by utilizing varying weight function, interaction domain, and tracer resting time distribution. This model is capable of characterizing both normal and anomalous tracer transport behaviors and converges to the space fractional CTRW model with a power-law weight function coupled with a global interaction domain. As a generalized tool, the ST-CTRW model bridges the gap between spatial nonlocal tracer transport processes at regional scales, extending from local to global levels. Key Points Transport properties; Groundwater; Hydrology; Fractional calculus; Integral transforms; Operator theory; Tracer diffusion; Flow dynamics; Sediment transport; Continuous time random walk －－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－ Dehua Wang, XiaoLi Ding, Lili Zhang, Xiaozhou Feng Publication information: Communications in Nonlinear Science and Numerical Simulation, Volume 143, 24 Feburary 2025. Abstract Stochastic wave equations with multiplicative fractional Brownian motions (fBms) provide a competitive means to describe wave propagation process driven by inner fractional noise. However, regularity theory and approximate solutions of such equations is still an unsolved problem until now. In this paper, we achieve some progress on the regularity and strong convergence of numerical approximations for a class of semilinear stochastic wave equations with multiplicative fBms. Firstly, we impose some suitable assumptions on the nonlinear term multiplied by fBms and its Malliavin derivatives, and analyze the temporal and spatial regularity of stochastic convolution operator under the assumptions for two cases H is an element of (0, 1/2) and H is an element of (1/2, 1). Using the obtained regularity results of the stochastic convolution operator, we further establish the regularity theory of mild solution of the equation, and reveal quantitatively the influence of Hurst parameter on the regularity of the mild solution. Besides that, we give a fully discrete scheme for the stochastic wave equation and analyze its strong convergence. Finally, two numerical examples are carried out to verify the theoretical findings. Keywords Semilinear stochastic wave equations; Fractional Brownian motions; Regularity analysisNumerical approximation; Strong convergence ========================================================================== The End of This Issue ∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽
Regularity and strong convergence of numerical approximations for stochastic wave equations with multiplicative fractional Brownian motions
https://doi.org/10.1016/j.cnsns.2025.108648
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