FDA Express Vol

Analysis and numerical approximation of tempered fractional calculus of variations problems
by: Almeida, Ricardo; Luisa Morgado, M.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 361 Pages: 1-12 Published: DEC 1 2019

An iterative multistep kernel based method for nonlinear Volterra integral and integro-differential equations of fractional order
by: Heydari, Mojgan; Shivanian, Elyas; Azarnavid, Babak; etc.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 361 Pages: 97-112 Published: DEC 1 2019

Fourier spectral exponential time differencing methods for multi-dimensional space-fractional reaction-diffusion equations
by: Alzahrani, S. S.; Khaliq, A. Q. M.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS Volume: 361 Pages: 157-175 Published: DEC 1 2019

Mittag-Leffler stability for a new coupled system of fractional-order differential equations with impulses
by: Li, Hui; Kao, YongGui
APPLIED MATHEMATICS AND COMPUTATION Volume: 361 Pages: 22-31 Published: NOV 15 2019

Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension
by: Zheng, Xiangcheng; Ervin, V. J.; Wang, Hong
APPLIED MATHEMATICS AND COMPUTATION Volume: 361 Pages: 98-111 Published: NOV 15 2019

Supplementary remark to 'Representations of acting processes and memory effects: General fractional derivative and its application to theory of heat conduction with finite wave speeds' [Applied Mathematics and Computation 346 (2019) 531-544]
by: Zhao, Dazhi; Luo, Maokang
APPLIED MATHEMATICS AND COMPUTATION Volume: 361 Pages: 175-176 Published: NOV 15 2019

A novel Legendre operational matrix for distributed order fractional differential equations
by: Pourbabaee, Marzieh; Saadatmandi, Abbas
APPLIED MATHEMATICS AND COMPUTATION Volume: 361 Pages: 215-231 Published: NOV 15 2019

Influence of multiple time delays on bifurcation of fractional-order neural networks
by: Xu, Changjin; Liao, Maoxin; Li, Peiluan; etc.
APPLIED MATHEMATICS AND COMPUTATION Volume: 361 Pages: 565-582 Published: NOV 15 2019

A finite difference scheme on graded meshes for time-fractional nonlinear Korteweg-de Vries equation
by: Shen, Jinye; Sun, Zhi-zhong; Cao, Wanrong
APPLIED MATHEMATICS AND COMPUTATION Volume: 361 Pages: 752-765 Published: NOV 15 2019

Disturbance rejection of fractional-order T-S fuzzy neural networks based on quantized dynamic output feedback controller
by: Karthick, S. A.; Sakthivel, R.; Ma, Y. K.; etc.
APPLIED MATHEMATICS AND COMPUTATION Volume: 361 Pages: 846-857 Published: NOV 15 2019

Note on a nonlocal Sturm-Liouville problem with both right and left fractional derivatives
by: Li, Jing; Qi, Jiangang
APPLIED MATHEMATICS LETTERS Volume: 97 Pages: 14-19 Published: NOV 2019

Necessary conditions for the existence of positive solutions to fractional boundary value problems at resonance
by: Wang, Yongqing
APPLIED MATHEMATICS LETTERS Volume: 97 Pages: 34-40 Published: NOV 2019

Multiplicity results of nonlinear fractional magnetic Schrodinger equation with steep potential
by: Mao, Suzhen; Xia, Aliang
APPLIED MATHEMATICS LETTERS Volume: 97 Pages: 73-80 Published: NOV 2019

The finite volume scheme preserving maximum principle for two-dimensional time-fractional Fokker-Planck equations on distorted meshes
by: Yang, Xuehua; Zhang, Haixiang; Zhang, Qi; etc.
APPLIED MATHEMATICS LETTERS Volume: 97 Pages: 99-106 Published: NOV 2019

On the boundedness of nonoscillatory solutions of certain fractional differential equations with positive and negative terms
by: Grace, Said R.; Graef, John R.; Tunc, Ercan
APPLIED MATHEMATICS LETTERS Volume: 97 Pages: 114-120 Published: NOV 2019

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Call for Papers

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The 11th International Conference on Non-Integer Order Calculus And Its Applications (RRNR 2019)

(September 12-13, 2019, Cze¸stochowa, Poland)
Website: http://im.pcz.pl/rrnr2019

The RRNR 2019 – 11th INTERNATIONAL CONFERENCE ON NON-INTEGER ORDER CALCULUS AND ITS APPLICATIONS will be held in the Czestochowa University of Technology, Częstochowa, Poland, 12-13 September 2019.

A characteristic feature of the conference RRNR is no conference fee, however the participants cover the cost of travel and accommodation in Częstochowa.

The conference will include four main themes as follows

1. Mathematical foundations
2. Dynamic system modeling
3. Fractional-order systems analysis
4. Fractional-order closed-loop systems synthesis
5. Application of fractional calculus in mechanics
　

Brief History of the Conference
In June 2009 the Seminar "Rachunek Różniczkowy Niecałkowitego Rzędu i jego Zastosowania" (RRNR) (English name: Non-integer Order Calculus and Its Applications) started as the first Polish annual symposium in Łódź, Poland. Second seminar took place in Częstochowa, Poland in 2010. All subsequent seminars took place in Poland in different scientific centres. In 2016 the Seminar was renamed The Conference on Non-integer Order Calculus and Its Applications. The last edition of the conference took place last year in the Bialystok University of Technology, Białystok, Poland.
　

All details on this conference are now available at: http://im.pcz.pl/rrnr2019/.

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Books

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High Accuracy Algorithm for the Differential Equations Governing Anomalous Diffusion — Algorithm and Models for Anomalous Diffusion

(Authors: Weihua Deng and Zhijiang Zhang )

Details: https://www.worldscientific.com/worldscibooks/10.1142/10095

Introduction

The aim of this book is to extend the application field of 'anomalous diffusion', and describe the newly built models and the simulation techniques to the models.

The book first introduces 'anomalous diffusion' from the statistical physics point of view, then discusses the models characterizing anomalous diffusion and its applications, including the Fokker–Planck equation, the Feymann–Kac equations describing the functional distribution of the anomalous trajectories of the particles, and also the microscopic model — Langevin type equation. The second main part focuses on providing the high accuracy schemes for these kinds of models, and the corresponding convergence and stability analysis.

Chapters

-Introduction

-Mathematical Models

-Numerical Methods for the Time Fractional Differential Equations

-High Order Finite Difference Methods for the Space Fractional PDEs

-Variation Numerical Method for the Space Fractional PDEs

Readership: Graduate students and researchers in Numerical Analysis, Integral Equations, Partial Differential Equations, Statistical Physics, Computational Physics.

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Journals

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Fractional Calculus and Applied Analysis

(Volume 22, Issue 2 (Apr 2019), Issue 3 (Jun 2019))

The flaw in the conformable calculus: It is conformable because it is not fractional
Abdelhakim, Ahmed A.

The failure of certain fractional calculus operators in two physical models
Ortigueira, Manuel D. / Martynyuk, Valeriy / Fedula, Mykola / Machado, J. Tenreiro

Inverse problems for a class of degenerate evolution equations with Riemann – Liouville derivative
Fedorov, Vladimir E. / Nazhimov, Roman R.

On Riesz derivative
Cai, Min / Li, Changpin

A note on fractional powers of strongly positive operators and their applications
Ashyralyev, Allaberen / Hamad, Ayman

Semi-fractional diffusion equations
Kern, Peter / Lage, Svenja / Meerschaert, Mark M.

Extremum principle for the Hadamard derivatives and its application to nonlinear fractional partial differential equations
Kirane, Mokhtar / Torebek, Berikbol T.

Well-posedness of fractional degenerate differential equations in Banach spaces
Bu, Shangquan / Cai, Gang

Structure factors for generalized grey Browinian motion
da Silva, José L. / Streit, Ludwig

Linear stationary fractional differential equations
Nosov, Valeriy / Meda-Campaña, Jesús Alberto

Perfect control for right-invertible Grünwald-Letnikov plants – an innovative approach to practical implementation
Hunek, Wojciech Przemysław

On fractional differential inclusions with Nonlocal boundary conditions
Castaing, Charles / Godet-Thobie, C. / Phung, Phan D. / Truong, Le X.

On solutions of linear fractional differential equations and systems thereof
Dorjgotov, Khongorzul / Ochiai, Hiroyuki / Zunderiya, Uuganbayar

Existence of mild solution of a class of nonlocal fractional order differential equation with not instantaneous impulses
Borah, Jayanta / Nandan Bora, Swaroop

A CAD-based algorithm for solving stable parameter region of fractional-order systems with structured perturbations
Yang, Jing / Hou, Xiaorong / Luo, Min

On representation and interpretation of Fractional calculus and fractional order systems
García-Sandoval, Juan Paulo

The probabilistic point of view on the generalized fractional partial differential equations
Kolokoltsov, Vassili N.

A system of coupled multi-term fractional differential equations with three-point coupled boundary conditions
Ahmad, Bashir / Alghamdi, Najla / Alsaedi, Ahmed / Ntouya, Sotiris K.

Fractal convolution: A new operation between functions
Navascués, María A. / Massopust, Peter R.

Unique continuation principle for the one-dimensional time-fractional diffusion equation
Li, Zhiyuan / Yamamoto, Masahiro

Asymptotics of eigenvalues for differential operators of fractional order
Kukushkin, Maksim V.

The asymptotic behaviour of fractional lattice systems with variable delay
Liu, Linfang / Caraballo, Tomás / Kloeden, Peter E.

On fractional asymptotical regularization of linear ill-posed problems in hilbert spaces
Zhang, Ye / Hofmann, Bernd

Weighted Hölder continuity of Riemann-Liouville fractional integrals – Application to regularity of solutions to fractional cauchy problems with Carathéodory dynamics
Bourdin, Loïc

Green’s functions, positive solutions, and a Lyapunov inequality for a caputo fractional-derivative boundary value problem
Meng, Xiangyun / Stynes, Martin

Finite element approximations for fractional evolution problems
Acosta, Gabriel / Bersetche, Francisco M. / Borthagaray, Juan Pablo

Stochastic diffusion equation with fractional Laplacian on the first quadrant
Sanchez-Ortiz, Jorge / Ariza-Hernandez, Francisco J. / Arciga-Alejandre, Martin P. / Garcia-Murcia, Eduard A.

Stability of fractional variable order difference systems
Mozyrska, Dorota / Oziablo, Piotr / Wyrwas, Małgorzata

Chaotic dynamics of fractional Vallis system for El-Niño
Deshpande, Amey / Daftardar-Gejji, Varsha

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Communications in Nonlinear Science and Numerical Simulation

(Selected)

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

Fractional comparison method and asymptotic stability results for multivariable fractional order systems
Bichitra Kumar Lenka

Variable order fractional systems
Manuel D. Ortigueira, Duarte Valério, J. Tenreiro Machado

Modeling biological systems with an improved fractional Gompertz law
Luigi Frunzo, Roberto Garra, Andrea Giusti, Vincenzo Luongo

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

Comments on various extensions of the Riemann-Liouville fractional derivatives : about the Leibniz and chain rule properties
Jacky Cresson, Anna Szafrańska

Fractional derivatives and negative probabilities
J. Tenreiro Machado

No nonlocality. No fractional derivative
Vasily E. Tarasov

Derivation of the nonlocal pressure form of the fractional porous medium equation in the hydrological setting
Łukasz Płociniczak

On the fractional Cornu spirals
Constantin Milici, J. Tenreiro Machado, Gheorghe Drăgănescu

Direct transcription methods based on fractional integral approximation formulas for solving nonlinear fractional optimal control problems
Abubakar Bello Salati, Mostafa Shamsi, Delfim F. M. Torres

On the ψ-Hilfer fractional derivative
J. Vanterler da C. Sousa, E. Capelas de Oliveira

Stability analysis of fractional delayed equations and its applications on consensus of multi-agent systems
Song Liu, Ran Yang, Xian-Feng Zhou, Wei Jiang, Xiao-Wen Zhao

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

Fractional-order modeling of a diode
J. A. Tenreiro Machado, António M. Lopes

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Paper Highlight

A Survey of Models of Ultraslow Diffusion in Heterogeneous Materials

Yingjie Liang, Shuhong Wang, Wen Chen, Zhifang Zhou and Richard L. Magin

Publication information: Applied Mechanics Reviews 71(4), July 09, 2019

http://appliedmechanicsreviews.asmedigitalcollection.asme.org/article.aspx?articleid=2737005

　

Abstract

Ultraslow diffusion is characterized by a logarithmic growth of the mean squared displacement (MSD) as a function of time. It occurs in complex arrangements of molecules, microbes, and many-body systems. This paper reviews mechanical models for ultraslow diffusion in heterogeneous media from both macroscopic and microscopic perspectives. Macroscopic models are typically formulated in terms of a diffusion equation that employs noninteger order derivatives (distributed order, structural, and comb models (CM)) or employs a diffusion coefficient that is a function of space or time. Microscopic models are usually based on the continuous time random walk (CTRW) theory, but use a weighted logarithmic function as the limiting formula of the waiting time density. The similarities and differences between these models are analyzed and compared with each other. The corresponding MSD in each case is tabulated and discussed from the perspectives of the underlying assumptions and of real-world applications in heterogeneous materials. It is noted that the CMs can be considered as a type of two-dimensional distributed order fractional derivative model (DFDM), and that the structural derivative models (SDMs) generalize the DFDMs. The heterogeneous diffusion process model (HDPM) with time-dependent diffusivity can be rewritten to a local structural derivative diffusion model mathematically. The ergodic properties, aging effect, and velocity autocorrelation for the ultraslow diffusion models are also briefly discussed.

　

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Analytical and numerical study of Stokes flow problems for Hausdorff fluids

Xianglong Su, Wenxiang Xu, Wen Chen

Publication information: Communications in Nonlinear Science and Numerical Simulation, Available online 29 July 2019, 104932
https://www.sciencedirect.com/science/article/pii/S1007570419302539?via=ihub

Abstract

Flow problem for non-Newtonian fluid has drawn considerable attention over past decades. In this study, we theoretically and numerically investigate the unsteady Stokes’ flow problem of the viscoelastic fluid. The constitutive equation of the viscoelastic fluid is modified from the Newtonian fluid by introducing the Hausdorff derivative, called the Hausdorff fluid. It should be noted that the Hausdorff fluid degenerates to the Newtonian fluid when the derivative order α equals to unity (α=1). The analytical solutions for velocity field are derived by employing the Fourier sine transform and transformation of variables. The obtained analytical solutions are validated by the finite element simulation. Results show that the Hausdorff fluid with small derivative order α has high propagation velocity and flow velocity. Compared with Stokes’ flow problems for other non-Newtonian fluids, the Hausdorff fluid has the similar velocity distributions with the second grade (SG) fluid but different from the Maxwell (MX) fluid. In addition, the SG fluid has decreased propagation velocity while the MX fluid has increased propagation velocity in comparison with the Hausdorff fluid.

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The End of This Issue

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