FDA Express

FDA Express    Vol. 41, No. 2, Nov. 30, 2021

 

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 41_No 2_2021.pdf


 

◆  Latest SCI Journal Papers on FDA

(Searched on Nov. 30, 2021)

 

  Call for Papers

Operators of Fractional Calculus and Their Multi-Disciplinary Applications

Fractional Order Systems and Their Applications

 

◆  Books

General Fractional Derivatives with Applications in Viscoelasticity

 

◆  Journals

Communications in Nonlinear Science and Numerical Simulation

Nonlinear Dynamics

 

  Paper Highlight

Anomalous overland flow on hillslopes: A fractional kinematic wave model, its solutions and verification with data from laboratory observations

The electro-osmotic flow and heat transfer of generalized Maxwell fluids with distributed-order time-fractional characteristics in microtubules under an alternating field

 

  Websites of Interest

Fractal Derivative and Operators and Their Applications

Fractional Calculus & Applied Analysis

 

 

 

 

 

========================================================================

 Latest SCI Journal Papers on FDA

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

(Searched on Nov. 30, 2021)



 Robust control of congestion in computer networks: An adaptive fractional-order approach

By: Nasiri, I and Nikdel, N
EXPERT SYSTEMS WITH APPLICATIONS Volume: ‏ 190 Published: ‏ Mar 15 2022


 Modeling and parametric identification of Hammerstein systems with time delay and asymmetric dead-zones using fractional differential equations

By: Prasad, V and Mehta, U
MECHANICAL SYSTEMS AND SIGNAL PROCESSING Volume: ‏ 167 Published: ‏ Mar 15 2022


 A stable collocation approach to solve a neutral delay stochastic differential equation of fractional order

By: Banihashemi, S; Jafari, H and Babaei, A
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: ‏403         Published: ‏  Mar 15 2022


 Traveling Wave Solution of Bad and Good Modified Boussinesq Equations with Conformable Fractional-Order Derivative

By: N'Gbo, N and Xia, YH
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: ‏ 21 Issue: 1 Published: ‏  Mar 2022


 Numerical approaches to Caputo-Hadamard fractional derivatives with applications to long-term integration of fractional differential systems

By: Fan, EY; Li, CP and Li, ZQ
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: ‏ 106 Published: Mar 2022


 Group formalism of Lie transformations, conservation laws, exact and numerical solutions of non-linear time-fractional Black-Scholes equation

By: Rashidi, S; Hejazi, SR and Mohammadizadeh, F
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: ‏ 403 Published: ‏ MAR 15 2022


 A note on stability of fractional logistic maps

By:Mendiola-Fuentes, J and Melchor-Aguilar, D
APPLIED MATHEMATICS LETTERS Volume: 125 Published: Mar 2022


 Higher order numerical schemes for the solution of fractional delay differential equations

By: Gande, NR and Madduri, H
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: ‏ 402 Published: ‏ Mar 1 2022


 Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems

By: Peng, X; Wang, YJ and Zuo, ZQ
APPLIED MATHEMATICS AND COMPUTATION Volume: ‏ 415 Published: ‏ Feb 15 2022


 Stable numerical schemes for time-fractional diffusion equation with generalized memory kernel

By: Kedia, N; Alikhanov, AA and Singh, VK
APPLIED NUMERICAL MATHEMATICS Volume: ‏ 172 Issue:546-565 Published: Feb 2022


 High-order explicit conservative exponential integrator schemes for fractional Hamiltonian PDEs

By:Fu, YY; Hu, DD and Xu, ZZ
APPLIED NUMERICAL MATHEMATICS Volume: ‏172 Page: 315-331 Published: Feb 2022


 Noninstantaneous Impulsive Conformable Fractional Stochastic Delay Integro-Differential System with Rosenblatt Process and Control Function

By: Ahmed, HM
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: ‏ 21 Published: ‏ MAR 2022


 alpha-robust H-1-norm error estimate of nonuniform Alikhanov scheme for fractional sub-diffusion equation

By: Chen, H; Wang, Y and Fu, HF
APPLIED MATHEMATICS LETTERS Volume: ‏ 125 Published: ‏ Mar 2022


 On the extension problem for semiconcave functions with fractional modulus

By: Albano, P; Basco, V and Cannarsa, P
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS Volume: ‏ 216 Published: ‏MAR 2022


 A high-precision numerical approach to solving space fractional Gray-Scott model

By: Han, C; Wang, YL and Li, ZY
APPLIED MATHEMATICS LETTERS Volume: ‏ 125 Published: ‏ MAR 2022


 A fast algorithm for fractional Helmholtz equation with application to electromagnetic waves propagation

By: Belevtsov, NS and Lukashchuk, SY
APPLIED MATHEMATICS AND COMPUTATION Volume: ‏ 416 Published: ‏ MAR 1 2022


 On a Coupled Impulsive Fractional Integrodifferential System with Hadamard Derivatives

By: Alam, M; Zada, A and Riaz, U
QUALITATIVE THEORY OF DYNAMICAL SYSTEMS Volume: 21 Published: ‏ MAR 2022


 Subordination principle, Wright functions and large-time behavior for the discrete in time fractional diffusion equation

By:Abadias, L; Alvarez, E and Diaz, S
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Volume: ‏ 507 Published: MAR 1 2022


 Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems

By: Peng, X; Wang, YJ and Zuo, ZQ
APPLIED MATHEMATICS LETTERS Volume: 415 Published: ‏ FEB 15 2022

 

 

 

[Back]

 

==========================================================================

Call for Papers

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

Operators of Fractional Calculus and Their Multi-Disciplinary Applications

( A special issue of Fractal and Fractional )


Dear Colleagues: Current widespread interest in various families of fractional-order integral and derivative operators, such as those named after Riemann–Liouville, Weyl, Hadamard, Grunwald–Letnikov, Riesz, Erdélyi–Kober, Liouville–Caputo, and so on, have stemmed essentially from their demonstrated applications in numerous diverse areas of the mathematical, physical, chemical, engineering, and statistical sciences. These fractional-order operators provide interesting and potentially useful tools for solving ordinary and partial differential equations, as well as integral, differintegral, and integro-differential equations, the fractional-calculus analogues and extensions of each of these equations, and various other problems involving special functions of mathematical physics, applicable analysis and applied mathematics, as well as their extensions and generalizations in one, two and more variables.

In this Special Issue, we invite and welcome review, expository, and original research articles dealing with recent advances in the theory of integrals and derivatives of fractional order and their multidisciplinary applications.

Keywords:

- operators of fractional integrals and fractional derivatives and their applications
- chaos and dynamical systems based upon fractional calculus
- fractional-order ODEs and PDEs
- fractional-order differintegral and integro-differential equations
- integrals and derivatives of fractional order associated with special functions of mathematical physics and applied mathematics
- identities and inequalities involving fractional-order integrals and fractional-order derivatives


Organizers:

Prof. Dr. Hari Mohan Srivastava
Guest Editors

Important Dates:

Deadline for manuscript submissions: 15 December 2021.

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



Fractional Order Systems and Their Applications

( A special issue of Fractal and Fractional )


Dear Colleagues: Fractional calculus (FC) generalizes the concepts of derivative and integral to non-integer orders. It was introduced by Leibniz (1646–1716), but remained a purely mathematical exercise for a long time, despite the original contributions of important mathematicians, physicists, and engineers. FC experienced rapid development during the last few decades both in mathematics and applied sciences, being recognized as an excellent tool to describe complex dynamics. From this perspective, several models governing physical phenomena in the area of science and engineering have been reformulated in light of FC for better reflecting their non-local, frequency- and history-dependent properties. Applications of FC include modeling of diffusion, viscoelasticity, and relaxation processes in fluid mechanics, dynamics of mechanical, electronic and biological systems, signal processing, control, and others.

The Special Issue focuses on original and new research results on fractional order theory and applications. Manuscripts addressing novel theoretical issues, as well as those on more specific applications, are welcome.



Keywords:

- fractals
- fractional calculus
- complex systems
- chaos
- modeling
- identification
- control


Organizers:

Prof. Dr. António M. Lopes
Dr. Liping Chen
Guest Editor

Important Dates:

Deadline for manuscript submissions: 23 January 2022.

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





[Back]

 

 

===========================================================================

Books

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

Fractional Derivatives with Mittag-Leffler Kernel

( Authors: José Francisco, GómezLizeth TorresRicardo, Fabricio Escobar )

Details:https://doi.org/10.1007/978-3-030-11662-0

Book Description:

This book offers a timely overview of fractional calculus applications, with a special emphasis on fractional derivatives with Mittag-Leffler kernel. The different contributions, written by applied mathematicians, physicists and engineers, offers a snapshot of recent research in the field, highlighting the current methodological frameworks together with applications in different fields of science and engineering, such as chemistry, mechanics, epidemiology and more. It is intended as a timely guide and source of inspiration for graduate students and researchers in the above-mentioned areas.

Author Biography:

José Francisco Gómez1: CONACYT-Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca,Mexico
Lizeth Torres: CONACYT-Instituto de Ingeniería, Universidad Nacional Autónoma de México, Mexico City, Mexico
Ricardo Fabricio Escobar: Tecnológico Nacional de México, Centro Nacional de Investigación y Desarrollo Tecnológico, Cuernavaca, Mexico


Contents:

Front Matter

Reproducing Kernel Method for Fractional Derivative with Non-local and Non-singular Kernel
Introduction; Fractional Derivative with Non-local and Non-singular Kernel; Reproducing Kernel Hilbert Spaces; Main Results; Applications; Conclusions; References;

Necessary and Sufficient Optimality Conditions for Fractional Problems Involving Atangana–Baleanu’s Derivatives
Introduction; Preliminaries Fractional Variational Principles Within Fractional Atangana–Baleanu’s Derivatives; The Fractional Canonical Momenta; Some Generalization; Fractional Variational Principles and Constrained Systems Within Atangana–Baleanu’s Derivatives; Sufficient Conditions; Fractional Optimal Control Problem Involving Atangana–Baleanu’s Derivatives; Conclusions; References;

Variable Order Mittag–Leffler Fractional Operators on Isolated Time Scales and Application to the Calculus of Variations
Introduction; Fractional Sums and Differences of Variable Order; Summation by Parts for Variable Order Fractional Operators; Variable Order Fractional Variational Principles; Notes; References;

Modeling and Analysis of Fractional Leptospirosis Model Using Atangana–Baleanu Derivative
Introduction; Preliminaries; Leptospirosis Model with AB Derivative; Existence of Solutions for Fractional Leptospirosis Infection Model; Numerical Results; Conclusion; References;

Dual Fractional Analysis of Blood Alcohol Model Via Non-integer Order Derivatives
Introduction; Fractional Modeling of Blood Alcohol Model; Solution of the Fractional Blood Alcohol Model; Results and Conclusions; Notes; References;

Parameter Estimation of Fractional Gompertz Model Using Cuckoo Search Algorithm
Introduction; Basic Definitions; Cuckoo Search; Tests; Conclusions; Notes; References;

Existence and Uniqueness Results for a Novel Complex Chaotic Fractional Order System
Introduction; New Fractional Derivative with Non-singular and Non-local Kernel; Picard’s Existence and Uniqueness Theorem for Atangana–Baleanu Fractional Complex System in Caputo Sense; Numerical Scheme; Conclusion; References;

On the Chaotic Pole of Attraction with Nonlocal and Nonsingular Operators in Neurobiology
Introduction to the Model; Some Definitions on the Non-integer Order Derivatives; Generalities on the Haar Wavelets Method for Non-linear Differential Equations; Haar Wavelets Numerical Method for the System; Error Analysis and Convergence for the Numerical Approximation by Haar Wavelets Method; Application to Particular Cases of HR Neuron with External Current Input; Conclusion; Notes; References;

Modulating Chaotic Oscillations in Autocatalytic Reaction Networks Using Atangana–Baleanu Operator
Introduction; Solvability of the Model by Means of Haar Wavelets; Error Analysis and Convergence; Applications to Biochemical Systems of Four-Component Networks: Period-Doubling Bifurcations, Chaos and Interpretations; Concluding Remarks; Notes; References;

Development and Elaboration of a Compound Structure of Chaotic Attractors with Atangana–Baleanu Operator
Introduction; A Note on Haar wavelets; Solvability of the Model; Convergence Results; Simulations and Discussion on Mechanism of Forming the “Fractional” Attractors; Concluding Remarks; References;

On the Atangana–Baleanu Derivative and Its Relation to the Fading Memory Concept: The Diffusion Equation Formulation
Introduction; Necessary Background; Diffusion Equation in Terms of ABR Derivative; Discussion; References;

Numerical Solutions and Pattern Formation Process in Fractional Diffusion-Like Equations
Introduction; Some Basic Properties of Fractional Calculus; Numerical Methods; Main Equations and Numerical Experiments; Conclusion; References;

Heat Transfer Analysis in Ethylene Glycol Based Molybdenum Disulfide Generalized Nanofluid via Atangana–Baleanu Fractional Derivative Approach
Introduction; Mathematical Formulation; Solution of the Problem; Nusselt Number; Parametric Study; Concluding Remarks; References;

Atangana–Baleanu Derivative with Fractional Order Applied to the Gas Dynamics Equations
Introduction; History of Fractional Order Derivatives Without Singular Kernel; Basic Idea of the Modified Homotopy Analysis Transform Method with New Atangana–Baleanu Derivative in Caputo Sense; Convergence Analysis of MHATM with New Atangana–Baleanu Derivative in Caputo Sense; Application of HATM with New Atangana–Baleanu Derivative in Caputo Sense to Time Fractional Gas Dynamics Equations; Conclusion; Notes; References;

New Direction of Atangana–Baleanu Fractional Derivative with Mittag-Leffler Kernel for Non-Newtonian Channel Flow
Introduction; Mathematical Formulation; Exact Analytical Solutions; Parametric Studies Through Graphs; Concluding Remarks; Notes; Appendix-A; References;

Exact Solutions for the Liénard Type Model via Fractional Homotopy Methods
Introduction; Preliminaries; Implementation of the Laplace Homotopy Perturbation Method via Liouville–Caputo and Atangana–Baleanu–Caputo Fractional Order Derivatives; Implementation of the Modified Homotopy Analysis Transform Method via Liouville–Caputo and Atangana–Baleanu–Caputo Fractional Order Derivatives; Conclusions; Notes; References;

Model of Coupled System of Fractional Reaction-Diffusion Within a New Fractional Derivative Without Singular Kernel
Introduction; New -HATM Solutions; Numerical Results; Conclusion; Notes; References;

Upwind-Based Numerical Approximation of a Space-Time Fractional Advection-Dispersion Equation for Groundwater Transport Within Fractured Systems
Introduction; Advection-Focused Space-Time Fractional Transport Equation with Atangana–Baleanu in Caputo Sense (ABC) Derivative; Upwind Numerical Approximation Schemes; Numerical Stability Analysis; Comparison of Numerical Stability; Conclusions; References;

Back Matter


[Back]

 

========================================================================

 Journals

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

Communications in Nonlinear Science and Numerical Simulation

 (Selected)

 


 Lucas polynomials based spectral methods for solving the fractional order electrohydrodynamics flow model

M. Nosrati Sahlan, H. Afshari


 On numerical approximations of fractional-order spiking neuron models

A. M. AbdelAty, M. E. Fouda, A. M. Eltawil


 Adaptive numerical solutions of time-fractional advection–diffusion–reaction equations

Alessandra Jannelli


 Razumikhin qualitative analyses of Volterra integro-fractional delay differential equation with caputo derivatives

John R. Graef, Cemil Tunç, Hamdullah Şevli


 Invariant analysis and conservation laws of the time-fractional b-family peakon equations

Zhi-Yong Zhang, Guo-Fang Li


 Similarity solutions of fractional parabolic boundary value problems with uncertainty

C.Vinothkumar, A.Deiveegan, J.J.Nieto, P.Prakash


 Fractional dynamics with non-local scaling

Vasily E. Tarasov


 A generalized fractional-order Chebyshev wavelet method for two-dimensional distributed-order fractional differential equations

Quan H. Do, Hoa T. B. Ngo, Mohsen Razzaghi


 Necklace beams carrying fractional angular momentum in fractional systems with a saturable nonlinearity

Liangwei Dong, Dongshuai Liu, Wei Qi, Linxue Wang, Hui Zhou, Ping Peng, Changming Huang


 Nonstationary response statistics of fractional oscillators to evolutionary stochastic excitation

Qianying Cao, Sau-Lon James Hu, Huajun Li


 Variable-order fractional calculus: A change of perspective

Roberto Garrappa, Andrea Giusti, Francesco Mainardi


 Analysis and discretization of a variable-order fractional wave equation

Xiangcheng Zheng, Hong Wang


 Fractional generalized cumulative entropy and its dynamic version

AntonioDi Crescenzo, Suchandan Kayal, Alessandra Meoli


 Numerical continuation for fractional PDEs: sharp teeth and bloated snakes

Noémie Ehstand, Christian Kuehn, Cinzia Soresina


 Fractional derivative resolution of the anomalous magnetic field diffusion through a ferromagnetic steel rod: Application to eddy current testing

B. Ducharne, B. Zhang, G. Sebald

[Back]

 

 

Nonlinear Dynamics

  (Selected)

 


  Correction to: A universal predictor–corrector algorithm for numerical simulation of generalized fractional differential equations

Zaid Odibat


 Correction to: New theories and applications of tempered fractional differential equations

Nazek A. Obeidat, Daniel E. Bentil


 Fractional difference inequalities with their implications to the stability analysis of nabla fractional order systems

Yiheng Wei


 Nonlinear analysis of a four-dimensional fractional hyper-chaotic system based on general Riemann–Liouville–Caputo fractal–fractional derivative

Yuhang Pan


 Study on initial value problem for fractional-order cubature Kalman filters of nonlinear continuous-time fractional-order systems

Chuang Yang, Zhe Gao, Yue Miao, Tao Kan


 Identification of fractional-order Hammerstein nonlinear ARMAX system with colored noise

Qian Zhang, Hongwei Wang, Chunlei Liu


 Fractional-order PIλD sliding mode control for hypersonic vehicles with neural network disturbance compensator

Yongzhi Sheng, Weijie Bai, Yuwei Xie


 Chaotic dynamics in a novel COVID-19 pandemic model described by commensurate and incommensurate fractional-order derivatives

Nadjette Debbouche, Adel Ouannas, Iqbal M. Batiha, Giuseppe Grassi


 A fractional-order multistable locally active memristor and its chaotic system with transient transition, state jump

Wenli Xie, Chunhua Wang, Hairong Lin


 Fractional-order sliding mode control based guidance law with impact angle constraint

Yongzhi Sheng, Zhuo Zhang, Lei Xia


 Inherent anti-interference in fractional-order autonomous coupled resonator

Yanwei Jiang, Bo Zhang, Wei Chen


 A universal predictor–corrector algorithm for numerical simulation of generalized fractional differential equations

Zaid Odibat


 New theories and applications of tempered fractional differential equations

Nazek A. Obeidat, Daniel E. Bentil


 On the soliton solutions for an intrinsic fractional discrete nonlinear electrical transmission line

Emmanuel Fendzi-Donfack, Jean Pierre Nguenang, Laurent Nana


 Impact of fear effect in a fractional-order predator–prey system incorporating constant prey refuge

Chandan Maji

 

[Back]

 

 

========================================================================

 Paper Highlight

Anomalous overland flow on hillslopes: A fractional kinematic wave model, its solutions and verification with data from laboratory observations

Ninghu Su, Fengbao Zhang  

Publication information: Journal of Hydrology: Available online 14 November 2021

https://doi.org/10.1016/j.jhydrol.2021.127202


Abstract

This paper analyses a fractional kinematic wave equation (fKWE) for overland flow and evaluates its solutions for applications using data from overland flow flumes with simulated rainfall in the laboratory. Solutions of fKWE presented have been derived for large time or when the Laplace transform variable s→0, which is one of the most important situations for overland flow. The solutions include expressions for the depth, velocity, and unit discharge, of overland flow. Fitting the approximate solution for the depth of overland flow to the data yields the values of the order of space-fractional derivatives, ρ, which is around ρ=1.5. It is found that ρ increases with the slope gradient and the rainfall intensity. The approximate order of ρ=1.5, which is about the average of order 1 for the advection equation and 2 for the diffusion equation, implies that diffusive mechanisms manifest in the overland flow. The findings mean that either an fKWE is used or a diffusion term is needed to account for dynamic forces in overland flow as the fKWE captures more physical mechanisms.


Keywords

Fractional kinematic wave equation; Overland flow; Analytical solutions; Kinematic and dynamic forces; Laboratory flow experiments

 

[Back]

 

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


The electro-osmotic flow and heat transfer of generalized Maxwell fluids with distributed-order time-fractional characteristics in microtubules under an alternating field

 Chenqing Feng, Botong Li, Xinhui Si, Wei Wang, and Jing Zhu

Publication information: Physics of Fluids: Published 18 November 2021 2021
https://doi.org/10.1063/5.0073752


 

Abstract

The electro-osmotic flow and heat transfer of a Maxwell fluid with distributed-order time-fractional characteristics in a microchannel under an alternating field is investigated, while considering viscous dissipation and Joule heating. The unsteady momentum and energy equations are computed numerically directly using the finite volume method. The accuracy of the numerical method is validated by comparison the constructed velocity distribution with the velocity distribution in previous references. With the time going on, oscillation of alternating current with a constant amplitude will afford periodic velocity distribution. The temperature will periodically increase. Furthermore, the velocity and temperature distributions characteristics of a Newtonian fluid, fractional Maxwell fluid, and generalized Maxwell fluid with time distribution are compared. Finally, the effects of different physical parameters K, S, Br, Ha, λ, Ω, ψ1, ψ2, Pr, and δ on the velocity and heat distributions under an alternating field are discussed.

Keywords:

Thermodynamic states and processes; Maxwell fluids; Microchannel; Energy equations; Viscoelastic fluid; Heat transfer; Electric currents; Finite volume methods; Electroosmosis

 

[Back]

 

==========================================================================

The End of This Issue

∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽