FDA Express Vol

Tarig Projected Differential Transform Method to Solve Fractional Nonlinear Partial Differential Equations
By: Bagyalakshmi, M; SaiSundarakrishnan, G
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA Volume: 38 Issue: 3 Pages: 23-46 Published: 2020

Regular Classes Involving a Generalized Shift Plus Fractional Hornich Integral Operator
By: Ibrahim, Rabha W.
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA Volume: 38 Issue: 2 Pages: 89-99 Published: 2020

Stability Analysis of Linear Conformable Fractional Differential Equations System with Time Delays
By: Mohammadnezhad, Vahid; Eslami, Mostafa; Rezazadeh, Hadi
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA Volume:38 Issue: 6 Pages: 159-171 Published: 2020

Operational Shifted Hybrid Gegenbauer Functions Method for Solving Multi-term Time Fractional Differential Equations
By: Seyedi, Nasibeh; Saeedi, Habibollah
BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA Volume: 38 Issue: 4 Pages:97-110 Published: 2020

Adaptive hybrid fuzzy output feedback control for fractional-order nonlinear systems with time-varying delays and input saturation
By: Song, Shuai; Park, Ju H.; Zhang, Baoyong; etc..
APPLIED MATHEMATICS AND COMPUTATION Volume: 364 Published: JAN 1 2020

General linear and spectral Galerkin methods for the Riesz space fractional diffusion equation
By: Xu, Yang; Zhang, Yanming; Zhao, Jingjun
APPLIED MATHEMATICS AND COMPUTATION Volume: 364 Published: JAN 1 2020

A new family of predictor-corrector methods for solving fractional differential equations
By: Kumar, Manoj; Daftardar-Gejji, Varsha
APPLIED MATHEMATICS AND COMPUTATION Volume: 363 Published: DEC 15 2019

Several effective algorithms for nonlinear time fractional models
By: Qin, Hongyu; Wu, Fengyan
APPLIED MATHEMATICS AND COMPUTATION Volume: 363 Published: DEC 15 2019

Existence and stability of a positive solution for nonlinear hybrid fractional differential equations with singularity
By: Al-Sadi, Wadhah; Huang Zhenyou; Alkhazzan, Abdulwasea
JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE Volume: 13 Issue: 1 Pages: 951-960 Published: DEC 11 2019

A FEM for an optimal control problem subject to the fractional Laplace equation
By: Dohr, Stefan; Kahle, Christian; Rogovs, Sergejs; etc..
CALCOLO Volume: 56 Issue: 4 Published: DEC 2019

Efficient solution of time-fractional differential equations with a new adaptive multi-term discretization of the generalized Caputo-Dzherbashyan derivative
By: Durastante, Fabio
CALCOLO Volume: 56 Issue: 4 Published: DEC 2019

Delay-dependent stability switches in fractional differential equations
By: Cermak, Jan; Kisela, Tomas
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 79 Published: DEC 2019

Identification for Hammerstein nonlinear systems based on universal spline fractional order LMS algorithm
By: Cheng, Songsong; Wei, Yiheng; Sheng, Dian; etc..
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 79 Published: DEC 2019

Parameters estimation using mABC algorithm applied to distributed tracking control of unknown nonlinear fractional-order multi-agent systems
By: Hu, Wei; Wen, Guoguang; Rahmani, Ahmed; ; etc..
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 79 Published: DEC 2019

Fractional derivative modeling for suspended sediment in unsteady flows
By: Li, Chunhao; Chen, Diyi; Ge, Fudong; etc..
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 79 Published: DEC 2019

Fractional derivatives and negative probabilities
By: Machado, J. Tenreiro
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 79 Published: DEC 2019

A high-gain observer with Mittag-Leffler rate of convergence for a class of nonlinear fractional-order systems
By: Martinez-Fuentes, O.; Martinez-Guerra, R.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 79 Published: DEC 2019

Derivation and solution of space fractional modified Korteweg de Vries equation
By: Nazari-Golshan, A.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 79 Published: DEC 2019

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Call for Papers

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Fractional Order Systems and Controls Conference 2019
　

((December 27-29, 2019, Jinan Shandong, China))

Deadline: October 10, 2019

All details on this conference are now available at: https://cms.amss.ac.cn/resources.php.

Consulting E-mail: fosc@sdu.edu.cn　

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Books

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The Variable-Order Fractional Calculus of Variations

(Authors: Ricardo Almeida, Dina Tavares, Delfim F. M. Torres)

Details: https://link.springer.com/book/10.1007/978-3-319-94006-9#about

Introduction

The Variable-Order Fractional Calculus of Variations is devoted to the study of fractional operators with variable order and, in particular, variational problems involving variable-order operators. This brief presents a new numerical tool for the solution of differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one, an approximation formula is obtained in terms of standard (integer-order) derivatives only. Estimations for the error of the approximations are also provided.

The contributors consider variational problems that may be subject to one or more constraints, where the functional depends on a combined Caputo derivative of variable fractional order. In particular, they establish necessary optimality conditions of Euler-Lagrange type. As the terminal point in the cost integral is free, as is the terminal state, transversality conditions are also obtained.

The Variable-Order Fractional Calculus of Variations is a valuable source of information for researchers in mathematics, physics, engineering, control and optimization; it provides both analytical and numerical methods to deal with variational problems. It is also of interest to academics and postgraduates in these fields, as it solves multiple variational problems subject to one or more constraints in a single brief.

Chapters

-Front Matter

-Fractional Calculus

-The Calculus of Variations

-Expansion Formulas for Fractional Derivatives

-The Fractional Calculus of Variations

-Back Matter

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Journals

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Communications in Nonlinear Science and Numerical Simulation

(Selected)

On the properties of some operators under the perspective of fractional system theory
Manuel D. Ortigueira, J. Tenreiro Machado

On selection of improved fractional model and control of different systems with experimental validation
Abhaya Pal Singh, Dipankar Deb, Himanshu Agarwal

Macroscale modeling the methanol anomalous transport in the porous pellet using the time-fractional diffusion and fractional Brownian motion: A model comparison
Alexey Zhokh, Peter Strizhak

Financial time series analysis based on fractional and multiscale permutation entropy
Jinyang Li, Pengjian Shang, Xuezheng Zhang

Fractional cumulative residual entropy
Hui Xiong, Pengjian Shang, Yali Zhang

Electromagnetic-based derivation of fractional-order circuit theory
Tomasz P. Stefański, Jacek Gulgowski

Derivation and solution of space fractional modified Korteweg de Vries equation
A. Nazari-Golshan

Finite energy Lyapunov function candidate for fractional order general nonlinear systems
Yan Li, Daduan Zhao, YangQuan Chen, Igor Podlubny, Chenghui Zhang

Fractional derivative modeling for suspended sediment in unsteady flows
Chunhao Li, Diyi Chen, Fudong Ge, Yangquan Chen

Can we split fractional derivative while analyzing fractional differential equations?
Sachin Bhalekar, Madhuri Patil

The Lorentz transformations and one observation in the perspective of fractional calculus
Daniel Cao Labora, António M. Lopes, J. A. Tenreiro Machado

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Advances in Water Resources

(Selected)

Impact of absorbing and reflective boundaries on fractional derivative models: Quantification, evaluation and application
Yong Zhang, Xiangnan Yu, Xicheng Li, James F.Kelly, HongGuang Sun, Chunmiao Zheng

Analytical Pore-Network Approach (APNA): A novel method for rapid prediction of capillary pressure-saturation relationship in porous media
Harris Sajjad Rabbani, Thomas Daniel Seers, Dominique Guerillot

A two-sided fractional conservation of mass equation
Jeffrey S. Olsen, Jeff Mortensen, Aleksey S. Telyakovskiy

Crossover from anomalous to Fickean behavior in infiltration and reaction in fractal porous media
F. D. A. Aarao Reis

FracFit: A robust parameter estimation tool for fractional calculus models
James F. Kelly, Diogo Bolster, Mark M. Meerschaert, Jennifer D. Drummond, Aaron I. Packman

Space-time duality for the fractional advection-dispersion equation
James F. Kelly, Mark M. Meerschaert

Experimental and Theoretical Evidence for Increased Ganglion Dynamics During Fractional Flow in Mixed-Wet Porous Media
Shuangmei Zou, Ryan T. Armstrong, Ji-Youn Arns, Christoph H. Arns, Furqan Le-Hussain

Fractional Models Simulating Non-Fickian Behavior in Four-Stage Single-Well Push-Pull Tests
Kewei Chen, Hongbin Zhan, Qiang Yang

Unified fractional differential approach for transient interporosity flow in naturally fractured media
Petro Babak, Jalel Azaiez

Pore-scale analysis of supercritical CO2-brine immiscible displacement under fractional-wettability conditions
Sahar Bakhshian, Seyyed Abolfazl Hosseini

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Paper Highlight

Two-dimensional fractional linear prediction

Tomas Skovranek, Vladimir Despotovic, Zoran Peric

Publication information: Computers & Electrical Engineering, Volume 77, July 2019, Pages 37-46

https://doi.org/10.1016/j.compeleceng.2019.04.021

Abstract

Linear prediction (LP) has been applied with great success in coding of one-dimensional, time-varying signals, such as speech or biomedical signals. In case of two-dimensional signal representation (e.g. images) the model can be extended by applying one-dimensional LP along two space directions (2D LP). Fractional linear prediction (FLP) is a generalisation of standard LP using the derivatives of non-integer (arbitrary real) order. While FLP was successfully applied to one-dimensional signals, there are no reported implementations in multidimensional space. In this paper two variants of two-dimensional FLP (2D FLP) are proposed and optimal predictor coefficients are derived. The experiments using various grayscale images confirm that the proposed 2D FLP models are able to achieve comparable performance in comparison to 2D LP using the same support region of the predictor, but with one predictor coefficient less, enabling potential compression.

　

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Simulating multi-dimensional anomalous diffusion in nonstationary media using variable-order vector fractional-derivative models with Kansa solver

Xiaoting Liu, HongGuang Sun, Yong Zhang, Chunmiao Zheng, Zhongbo Yu

Publication information: Advances in Water Resources, Volume 133, November 2019, 103423
https://doi.org/10.1016/j.advwatres.2019.103423

Abstract

Anomalous diffusion can be multiple dimensional and space dependent in large-scale natural media with evolving nonstationary heterogeneity, whose quantification requires an efficient technique. This research paper develops, evaluates, and applies variable-order, vector, spatial fractional-derivative equation (FDE) models with a Kansa solver, to capture spatiotemporal variation of super-diffusion along arbitrary angles (i.e., preferential pathways) in complex geological media. The Kansa approach is superior to the traditional Eulerian solvers in solving the vector FDE models, because it is meshless and can be conveniently extended to multi-dimensional transport processes. Numerical experiments show that the shape parameter, one critical parameter used in the Kansa solver, significantly affects the accuracy and convergence of the numerical solutions. In addition, the collocation nodes need to be assigned uniformly in the model domain to improve the numerical accuracy. Real-world applications also test the feasibility of this novel technique. Hence, the variable-order vector FDE model and the Kansa numerical solver developed in this study can provide a convenient tool to quantify complex anomalous transport in multi-dimensional and non-stationary media with continuously or abruptly changing heterogeneity, filling the knowledge gap in parsimonious non-local transport models developed in the last decades.

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