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

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Institute of Soft Matter Mechanics, Hohai University
For contribution: jyh17@hhu.edu.cn, fda@hhu.edu.cn
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◆  Latest SCI Journal Papers on FDA

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Operators of Fractional Calculus and Their Multi-Disciplinary Applications

Fractional Order Systems and Their Applications

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

 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

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

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

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

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

 A note on stability of fractional logistic maps

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

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

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

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

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

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

 On the extension problem for semiconcave functions with fractional modulus

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

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

 On a Coupled Impulsive Fractional Integrodifferential System with Hadamard Derivatives

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

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

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:

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:

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.

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

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

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