FDA Express Vol. 52, No. 2
FDA Express Vol. 52, No. 2, Aug. 31, 2024
All issues: http://jsstam.org.cn/fda/
Editors: http://jsstam.org.cn/fda/Editors.htm
Institute of Soft Matter Mechanics, Hohai University
For contribution: jyh17@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 52_No 2_2024.pdf
◆ Latest SCI Journal Papers on FDA
◆ Call for Papers
Fractional Mathematical Modelling: Theory, Methods and Applications
Fractional-Order Approaches in Automation: Models and Algorithms
◆ Books
◆ Journals
International Journal of Heat and Mass Transfer
◆ Paper Highlight
◆ 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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Averaging Principle for McKean-Vlasov SDEs Driven by FBMs
By: Zhang, TQ; Xu, Y; etc.
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: 24 Published: Feb 2025
By:Özarslan, MA
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 454 Published: Jan 15 2025
By:Yan, XB; Xu, ZQJ and Ma, Z
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 454 Published: Jan 15 2025
Euler wavelets method for optimal control problems of fractional integro-differential equations
By:Singh, A; Kanaujiya, A and Mohapatra, J
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 454 Published: Jan 15 2025
By:Gong, ZH; Liu, CY; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 454 Published: Jan 15 2025
By:Narayanan, G; Jeong, JH and Joo, YH
INFORMATION SCIENCES Volume:686 Published:Jan 2025
By:Zourmba, K; Effa, JY; etc.
MATHEMATICS AND COMPUTERS IN SIMULATION Volume:227 Pages:58-84 Published:Jan 2025
Approximate solution of multi-term fractional differential equations via a block-by-block method
By:Katani, R; Shahmorad, S and Conte, D
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume:453 Published: Jan 1 2025
By: Du, TS and Long, Y
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: 541 Published: Jan 1 2025
By:Ali, KK; Raslan, KR; etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume:18 Published: Dec 31 2024
By:Li, XZ; Sha, AM; etc.
INTERNATIONAL JOURNAL OF PAVEMENT ENGINEERING Volume: 25 Published: Dec 31 2024
By: Zhou, L; Liu, XH; etc.
JOURNAL OF OBSTETRICS AND GYNAECOLOGY Volume:44 Published: Dec 31 2024
By:Munir, A; Vivas-Cortez, M; etc.
MATHEMATICAL AND COMPUTER MODELLING OF DYNAMICAL SYSTEMS Volume: 30 Pages:543-566 Published: Dec 31 2024
The use of Hermite wavelet collocation method for fractional cancer dynamical system
By:Agrawal, K; Kumar, S; etc.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Volume: 32 Published:Dec 31 2024
A novel fractionalized investigation of tuberculosis disease
By:Meena, M; Purohit, M; etc.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Volume: 32 Published: Dec 31 2024
By:Zhang, W; Zhang, Y and Ni, JB
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Volume:32 Published: Dec 31 2024
Computational analysis of rabies and its solution by applying fractional operator
By:Alazman, I; Mishra, MN; etc.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Volume: 32 Published:Dec 31 2024
Novel derivative operational matrix in Caputo sense with applications
By:Zaidi, D; Talib, I; etc.
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 18 Published: Dec 31 2024
Variational iteration method for n-dimensional time-fractional Navier-Stokes equation
By:Sharma, N; Alhawael, G;
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING Volume: 32 Published:Dec 31 2024
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Call for Papers
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Fractional Mathematical Modelling: Theory, Methods and Applications
( A special issue of Fractal and Fractional )
Dear Colleagues: The tools of fractional calculus serve as a new resource that is applicable in fields, including physics, fluid mechanics, hydrology, material science, signal processing, engineering, chemistry, biology, medicine, finance, and social sciences. This Special Issue aims to highlight the recent advancements in fractional calculus theory, innovative methodologies, and potential applications. We specifically invite authors to submit high-quality research that delves into the analysis of fractional differential/integral equations, the exploration of new definitions for fractional derivatives, the development of numerical methods to solve fractional equations, and the examination of applications in physical systems governed by fractional differential equations. The scope extends to include various other captivating research topics as well.
Keywords:
- Fractional differential and integral equations
- New fractional operators and their properties
- Existence and uniqueness of solutions
- Analytical and numerical methods
- Stability analysis
- Fractional calculus in physics
- Fractional dynamics in complex systems
- Applications to science and engineering
Organizers:
Dr. Faranak Rabiei
Dr. Dongwook Kim
Dr. Zeeshan Ali
Guest Editors
Important Dates:
Deadline for conference receipts: 30 September 2024.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/GY37SR31H3.
Fractional-Order Approaches in Automation: Models and Algorithms
( A special issue of Fractal and Fractional )
Dear Colleagues: Fractional calculus is a relatively new field of mathematics that deals with derivatives and integrals of non-integer orders. In recent years, there has been an increase in the popularity of this mathematical tool due to its ability to model and analyze complex physical systems that are difficult to describe using classical calculus. Fractional calculus has a wide range of applications, from control theory and signal processing to image analysis and finance. In this Special Issue of the journal Fractal and Fractional, we will explore the latest developments and applications of fractional calculus in various fields. These include, but are not limited to, biomedicine, materials science, and engineering. We will also showcase the latest advances in numerical methods and algorithms for solving fractional-order differential equations, which are the cornerstone of many applications in the field. Overall, this Special Issue aims to provide readers with a comprehensive overview of the current state of the art in fractional calculus and its applications.
In the realm of current automated control, fractional-order approximation has countless uses, including state estimating, controller design for linear and nonlinear systems, and the development of more precise mathematical models.
With this Special Issue, we hope to delve more deeply into the theory, design, implementation, and use of fractional-order approaches in the modeling and automation of dynamic systems across a variety of fields.
Topics of interest include, but are not limited to:
- Design of fractional-order control systems for high-power electrical systems. - Modeling, control, and stability of fractional-order systems.
- Fractional-order chaotic systems.
- Control of fractional-order chaotic systems.
- Applications of fractional-order systems in engineering.
- Fractional impulsive systems.
- Deterministic and stochastic fractional-order nonlinear systems.
- Filters, observers, and approximations of nonlinear systems using fractional derivatives.
- Fractional sliding mode control.
- Geometric control for fractional systems.
Keywords:
- Fractional-order systems
- Fractional-order control systems
- Fractional filtering
- Geometric interpretation of fractional-order calculus
- System identifications
- Fractional derivatives
- Neural networks using fractional-order calculus
Organizers:
Dr. Abraham Efraim Rodriguez Mata
Dr. Jesús Alfonso Medrano-Hermosillo
Dr. Pablo Antonio López-Pérez.
Guest Editors
Important Dates:
Deadline for manuscript submissions: 30 September 2024.
All details on this conference are now available at: https://www.mdpi.com/journal/fractalfract/special_issues/UX66WF5419.
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Books
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( Authors: Yuriy Povstenko )
Details:https://doi.org/10.1007/978-3-031-64587-7
Book Description:
This new edition offers expanded coverage of fractional calculus, including Riemann–Liouville fractional integrals, Riemann–Liouville and Caputo fractional derivatives, Riesz fractional operators, and Mittag-Leffler and Wright functions. Additionally, it provides a comprehensive examination of fractional heat conduction and related theories of thermoelasticity. Readers will gain insights into the concepts of time and space nonlocality and their impact on the generalizations of Fourier's law in thermoelasticity. This edition presents a detailed formulation of the problem of heat conduction in different domains and the associated thermal stresses, covering topics such as the fundamental solution to the Dirichlet problem, constant boundary conditions for temperature, and the fundamental solution to the physical Neumann problem. New insights into time-harmonic heat impact on the boundary have also been added. Cracks in the framework of fractional thermoelasticity are also considered.
Author Biography:
Yuriy Povstenko, Department of Mathematics and Computer Science, Jan Długosz University, Częstochowa, Poland
Contents:
Front Matter
Essentials of Fractional Calculus
Abstract; Riemann–Liouville Fractional Integrals; Riemann–Liouville and Caputo Fractional Derivatives; Riesz Fractional Operators; Mittag-Leffler Functions and Wright Function; References;
Fractional Heat Conduction and Related Theories of Thermoelasticity
Abstract; Material Continuum. Balance Equations; Constitutive Equations; Time and Space Nonlocality; Nonlocal Generalizations of the Fourier Law; Theories of Fractional Thermoelasticity; Initial and Boundary Conditions; Representation of Thermal Stresses; References;
Thermoelasticity Based on Time-Fractional Heat Conduction Equation in Polar Coordinates
Abstract; Fundamental Solutions to Axisymmetric Problems for an Infinite Solid; Delta-Pulse at the Origin; Radial Heat Conduction in a Cylinder and Associated Thermal Stresses; Radial Heat Conduction in an Infinite Medium with a Cylindrical Hole; References;
Axisymmetric Problems in Cylindrical Coordinates
Abstract; Thermal Stresses in a Long Cylinder; Thermal Stresses in an Infinite Medium with a Long Cylindrical Hole; Axisymmetric Problems for a Half-Space; References;
Thermoelasticity Based on Time-Fractional Heat Conduction Equation in Spherical Coordinates
Abstract; Fundamental Solutions to Central Symmetric Problems in an Infinite Solid; Delta-Pulse at the Origin; Radial Heat Conduction in a Sphere and Associated Thermal Stresses; Heat Conduction in a Body with a Spherical Cavity and Associated Thermal Stresses; References;
Thermoelasticity Based on Space-Time-Fractional Heat Conduction Equation
Abstract; Fundamental Solutions to Axisymmetric Problems in Polar Coordinates; Axisymmetric Solutions in Cylindrical Coordinates; Fundamental Solutions to Central Symmetric Problems in Spherical Coordinates; References;
Thermoelasticity Based on Fractional Telegraph Equation
Abstract; Time-Fractional Telegraph Equation; Solution in the Axially Symmetric Case; Solution in the Central Symmetric Case; Space-Time-Fractional Telegraph Equation; References;
Fractional Thermoelasticity of Thin Shells
Abstract; Thin Shells; Averaged Heat Conduction Equation; Generalized Boundary Conditions of Nonperfect Thermal Contact; Fractional Heat Conduction in Two Semi-infinite Solids Connected by Thin Intermediate Layer; Notes; References;
Fractional Advection-Diffusion Equation and Associated Diffusive Stresses
Abstract; The Fokker–Planck Equation; Space-Time-Fractional Advection-Diffusion Equation in the Case of One Spatial Variable According Two Approaches; Theory of Diffusive Stresses; Time-Fractional Advection-Diffusion Equation in a Plane; Time-Fractional Advection-Diffusion in a Space; References;
Cracks in the Framework of Fractional Thermoelasticity
Abstract; A Plane with a Line Crack; An Infinite Plane Containing an External Crack; A Solid with a Penny-Shaped Crack; An External Circular Crack in an Infinite Solid; Appendix: Integrals; References;
Fractional Nonlocal Elasticity
Abstract; Introduction; Fundamental Equations of Fractional Nonlocal Elasticity; Screw Dislocation in the Framework of Fractional Nonlocal Elasticity; Edge Dislocation in the Framework of Fractional Nonlocal Elasticity; Point Defect in a Fractional Nonlocal Elastic Solid; Appendix A: Integrals; Appendix B: Laplacian of the Stress Tensor in Cylindrical Coordinates; Appendix C: Laplacian of the Stress Tensor in Spherical Coordinates; References;
Back Matter
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Journals
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(Selected) Xiang Wu, Xujun Yang, Da-Yan Liu & Chuandong Li Xinyu Zhao, Li Li & Fajun Yu Zaid Odibat Jose S. Cánovas Wenjie Qing & Binfeng Pan Shupeng Wang, Hui Zhang & Xiaoyun Jiang Che Han & Xing Lü Tahar Haddad, Sarra Gaouir & Abderrahim Bouach Evren Tanriover, Ahmet Kiris, Burcu Tunga & M. Alper Tunga Lorenz Josue Oliva-Gonzalez & Rafael Martínez-Guerra K. S. Vishnukumar, S. M. Sivalingam, Hijaz Ahmad & V. Govindaraj J. Alberto Conejero, Òscar Garibo-i-Orts & Carlos Lizama Mehran Rahmani & Sangram Redkar Guohui Li, Ruiting Xie & Hong Yang Hanshu Chen, Guohai Chen, Zeng Meng & Dixiong Yang
A new fractional derivative operator with a generalized exponential kernel
Modified fractional homotopy method for solving nonlinear optimal control problems
Fractional physics-informed neural networks for time-fractional phase field models
Novel patterns in the space variable fractional order Gray–Scott model
Well-posedness and optimal control of a nonsmooth fractional dynamical system
A novel image denoising technique with Caputo type space–time fractional operators
State estimation-based parameter identification for a class of nonlinear fractional-order systems
Controllability of the time-varying fractional dynamical systems with a single delay in control
Inferring the fractional nature of Wu Baleanu trajectories
Fractional robust data-driven control of nonlinear MEMS gyroscope
Detection method of ship-radiated noise based on fractional-order dual coupling oscillator
International Journal of Heat and Mass Transfer
( Selected )
A. Somer, S. Galovic, etc.
A. Somer, S. Galovic, etc.
Y.W. Wang, J. Chen, etc.
Two-temperature time-fractional model for electron-phonon coupled interfacial thermal transport
Milad Mozafarifard, Yiliang Liao, etc.
Fractional telegraph equation under moving time-harmonic impact
Yuriy Povstenko, Martin Ostoja-Starzewski
From continuous-time random walks to the fractional Jeffreys equation: Solution and properties
Emad Awad, Trifce Sandev, etc.
Xiaoping Wang, Haitao Qi, etc.
Shupeng Wang, Hui Zhang, Xiaoyun Jiang
A general non-Fourier Stefan problem formulation that accounts for memory effects
Vaughan R. Voller, Sabrina Roscani
Dongbao Zhou, Yong Zhang, HongGuang Sun, Donald M. Reeves.
Qiang Xi, Zhuojia Fu, etc.
Convolved energy variational principle in heat diffusionn
B. T. DarrallG. F. Dargush
Generalized Boltzmann transport theory for relaxational heat conduction
Shu-Nan Li, Bing-Yang Cao
Emad Awad
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Paper Highlight
Convection heat and mass transfer of non-Newtonian fluids in porous media with Soret and Dufour effects using a two-sided space fractional derivative model
Yuehua Jiang, HongGuang Sun, Yong Zhang
Publication information: Computers & Mathematics with Applications, Volume 173 , 1 November 2024, Pages 74-86
https://doi.org/10.1016/j.camwa.2024.08.004
Abstract
Non-Newtonian fluids within heterogeneous porous media may give rise to complex spatial energy and mass distributions owing to non-local mechanisms, the modeling of which remains unclear. This study investigates the natural convection heat and mass transfer of non-Newtonian fluids in porous media, considering the Soret and Dufour effects. A strongly coupled model is developed to quantify the coupled transport of energy and reactive pollutants with the non-Newtonian fluid. The constitutive equation for the non-Newtonian fluid is described by a two-sided Caputo type space fractional velocity gradient. The governing equation, with a symmetric diffusion term, is effectively solved using a stable and convergent shifted Grünwald–Letnikov formula. The influences of three important parameters, which are the average skin friction coefficient, the average Nusselt number, and the Sherwood number, on fluid heat and mass transfer are calculated and analyzed. Numerical results reveal a significant interaction between the fractional derivative and the buoyancy ratio number, both of which affect the average skin friction coefficient. Furthermore, the average Nusselt number increases with the Dufour number while decreasing with the average Sherwood number. These findings enhance our understandings of the dynamics of energy and mass co-transport in non-Newtonian fluids, particularly in relation to their constitutive equation featuring spatial non-local properties.
Keywords
Natural convection, Porous media, Non-Newtonian fluids, Two-sided space fractional derivative
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Integrating classical and fractional calculus rheological models in developing hydroxyapatite-enhanced hydrogels
Paula Cambeses-Franco; Ramón Rial; Juan M. Ruso
Publication information: Physics of Fluids 36, 073101 (2024).
https://doi.org/10.1063/5.0213561
Abstract
This study presents a novel method for comprehending the rheological behavior of biomaterials utilized in bone regeneration. The focus is on gelatin, alginate, and hydroxyapatite nanoparticle composites to enhance their mechanical properties and osteoconductive potential. Traditional rheological models are insufficient for accurately characterizing the behavior of these composites due to their complexity and heterogeneity. To address this issue, we utilized fractional calculus rheological models, such as the Scott-Blair, Fractional Kelvin-Voigt, Fractional Maxwell, and Fractional Kelvin-Zener models, to accurately represent the viscoelastic properties of the hydrogels. Our findings demonstrate that the fractional calculus approach is superior to classical models in describing the intricate, time-dependent behaviors of the hydrogel-hydroxyapatite composites. Furthermore, the addition of hydroxyapatite not only improves the mechanical strength of hydrogels but also enhances their bioactivity. These findings demonstrate the potential of these composites in bone tissue engineering applications. The study highlights the usefulness of fractional calculus in biomaterials science, providing new insights into the design and optimization of hydrogel-based scaffolds for regenerative medicine.
Topics
Hydrogels, Biomaterials, Fractional calculus, Nanoparticle, Rheological properties, Viscoelastic properties, Tissue engineering
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