FDA Express

To be held in Kazan National Research Technical University named after A.N. Tupolev, KAI (former: Kazan Aviation Institute). Under the auspices of: Govn. of Republic of Tatarstan, Ministries of Education and Science of Russian Federation and of R. of Tatarstan, Federal State Budgetary Institution of Science, Tatarstan Academy of Sciences, Kotel’nikov Institute of radio Engn. and Electronics of RAS.

The conference is devoted to the 95-th anniversary of the outstanding scientist, the founder of the Kazan School of molecular electronics and application of the fractional operators in radioelectronics, Rector of the KAI (1967-1977), Chairman of the Supreme Council of the TASSR, Rashid Shakirovich Nigmatullin. For the contributions of Prof.R.S. Nigmatullin, read more in the Historical Survey:

D. Valerio, J. Tenreiro Machado, V. Kiryakova, Some pioneers of the applications of fractional calculus, Fract. Calc. Appl. Anal., Vol. 17, No 2 (2014), 552–578; 10.2478/s13540-014-0185-1;

https://www.degruyter.com/view/j/fca.2014.17.issue-2/issue-files/fca.2014.17.issue-2.xml.

Conference sections:

– Fractal elements and devices: analysis, synthesis and realizations;

– Fractal systems: analysis, synthesis and applications;

– Statistical methods of the treatment of the fractal signals and their applications;

– Molecular electronics, electrochemical systems, devices and detectors;

– Radioelectronics and telecommunication systems, noise immunity, electronic countermeasures;

– Technical electrodynamics, antennas technics and microwave technologies;

– Photonics and optical signals treatment;

– Dynamical chaos and physical fractals;

– Nanoelectronics and nanomaterials;

– Lasers and additive technologies;

– Quantum signals processing and quantum communications;

– Fractal paradigm in engineering education.

The organizers are planning publication in a foreign publishing house two books: – The “pioneering” works of the R.Sh. Nigmatullin; – Key publications of the invited speakers at ICNR-2018, related to the modern state of the fractional calculus and its application in technical and natural sciences.

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Latest Paper &Toolbox

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One-parameter fractional linear prediction

Author: Vladimir Despotovic, Tomas Skovranek, ZoranPeric

Publish information:

Computers & Electrical Engineering, Volume 69, July 2018, Pages 158-170.
https://doi.org/10.1016/j.compeleceng.2018.05.020

Abstract:

The one-parameter fractional linear prediction (FLP) is presented and the closed-form expressions for the evaluation of FLP coefficients are derived. Contrary to the classical first-order linear prediction (LP) that uses one previous sample and one predictor coefficient, the one-parameter FLP model is derived using the memory of two, three or four samples, while not increasing the number of predictor coefficients. The first-order LP is only a special case of the proposed one-parameter FLP when the order of fractional derivative tends to zero. Based on the numerical experiments using test signals (sine test waves), and real-data signals (speech and electrocardiogram), the hypothesis for estimating the fractional derivative order used in the model is given. The one-parameter FLP outperforms the classical first-order LP in terms of the prediction gain, having comparable performance with the second-order LP, although using one predictor coefficient less.

Key words: Linear prediction; Optimal prediction; Fractional calculus; Fractional derivative

MATLAB Toolbox "Fractional Linear Prediction" :

Author: Tomas Skovranek, Vladimir Despotovic
https://www.mathworks.com/matlabcentral/fileexchange/67867

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Books
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Luiz Roberto Evangelista, Ervin Kaminski Lenzi, Fractional Diffusion Equations and Anomalous Diffusion

Reviewer: Richard L. Magin

Book Description

The “and” in the title of this monograph is not simply an interdisciplinary connector, but serves as a proper coordinating conjunction with Boolean conviction. The authors, distinguished professors with decades of work in mathematical physics, here share their knowledge and perspective in a manner that is both tutorial and evocative. In fact, the book could be used as a text for graduate students and others who seek to learn more about how fractional order differential equations can be used to describe anomalous - non-Gaussian - diffusion. The emergence of fractional dynamics is illustrated for a variety of systems: integer, power law model parameters, fractional time or space orders and distributed fractional order. The first section provides an overview of fundamentals, a survey of fractional calculus and a very well written historical survey of diffusion, the continuous time random walk model, and the diffusion equation. The second section, then proceeds logically to present a sequence of diffusion models, each of which captures salient features of anomalous diffusion (memory, non-locality, Lévy flight, and the influence of surfaces and membranes). These models expand to include non-linear, distributed order and anisotropic cases, culminating with a chapter on the fractional Schrödinger equation. The final section of the book consists of two chapters on electrical impedance spectroscopy that connect the fractional order in the Poisson-Nernst-Planck model to electrode boundary conditions in the lumped-element circuit models (constant phase elements). The text is supplemented with numerous figures and an up to date list of references (380), each entry complete with title and authors.

Contents (10 Chapters):

– Preface;

– 1. Mathematical preliminaries;

– 2. A survey of the fractional calculus;

– 3. From normal to anomalous diffusion;

– 4. Fractional diffusion equations: elementary applications;

– 5. Fractional diffusion equations: surface effects;

– 6. Fractional nonlinear diffusion equation;

– 7. Anomalous diffusion: anisotropic case;

– 8. Fractional Schrödinger equations;

– 9. Anomalous diffusion and impedance spectroscopy;

– 10. The Poisson-Nernst-Planck anomalous (PNPA) models;

– References;

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Journals
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Fractional Calculus and Applied Analysis

(Vol. 21, No. 2 (2018))

Initial-boundary value problems for fractional diffusion equations with time-dependent coefficients

Kubica, Adam / Yamamoto, Masahiro

Analytical solutions for multi-term time-space fractional partial differential equations with nonlocal damping terms

Ding, Xiao-Li / Nieto, Juan J.

Fractional generalizations of Zakai equation and some solution methods

Umarov, Sabir / Daum, Fred / Nelson, Kenric

Stability analysis of impulsive fractional difference equations

Wu, Guo–Cheng / Baleanu, Dumitru

Mellin convolutions, statistical distributions and fractional calculus

Mathai, A. M.

Fractional wavelet frames in L2(ℝ)

Shah, Firdous A. / Debnath, Lokenath

Existence of solutions for a system of fractional differential equations with coupled nonlocal boundary conditions

Ahmad, Bashir / Luca, Rodica

Two point fractional boundary value problems with a fractional boundary condition

Lyons, Jeffrey W. / Neugebauer, Jeffrey T.

Large deviation principle for a space-time fractional stochastic heat equation with fractional noise

Yan, Litan / Yin, Xiuwei

Extension of Mikhlin multiplier theorem to fractional derivatives and stable processes

Karlı, Deniz

Noether symmetry and conserved quantity for fractional Birkhoffian mechanics and its applications

Song, Chuan-Jing / Zhang, Yi

Asymptotic behavior of mild solutions for nonlinear fractional difference equations

Xia, Zhinan / Wang, Dingjiang

Positive solutions to nonlinear systems involving fully nonlinear fractional operators

Niu, Pengcheng / Wu, Leyun / Ji, Xiaoxue

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Physica A: Statistical Mechanics and its Applications

(Selected)

Fractional conformable derivatives of Liouville–Caputo type with low-fractionality

V. F. Morales-Delgado, J. F. Gómez-Aguilar, R. F. Escobar-Jiménez, M. A. Taneco-Hernández

A new framework for multivariate general conformable fractional calculus and potential applications

Dazhi Zhao, Xueqin Pan, Maokang Luo

A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics

Dong Lei, Yingjie Liang, Rui Xiao

A time fractional convection–diffusion equation to model gas transport through heterogeneous soil and gas reservoirs

Ailian Chang, HongGuang Sun, Chunmiao Zheng, Bingqing Lu, Yong Zhang

Variable-order fractional MSD function to describe the evolution of protein lateral diffusion ability in cell membranes

Deshun Yin, Pengfei Qu

The resonant behavior in the oscillator with double fractional-order damping under the action of nonlinear multiplicative noise

Yan Tian, Lin-Feng Zhong, Gui-Tian He, Tao Yu, H. Eugene Stanley

NMR signals within the generalized Langevin model for fractional Brownian motion

Vladimír Lisý, Jana Tóthová

Suspension concentration distribution in turbulent flows: An analytical study using fractional advection–diffusion equation

Snehasis Kundu
Transport behaviors of locally fractional coupled Brownian motors with fluctuating interactions

Huiqi Wang, Feixiang Ni, Lifeng Lin, Wangyong Lv, Hongqiang Zhu

Investigation of the logarithmic-KdV equation involving Mittag-Leffler type kernel with Atangana–Baleanu derivative

Mustafa Inc, Abdullahi Yusuf, Aliyu Isa Aliyu, Dumitru Baleanu

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Paper Highlight

Colloquium: Fractional calculus view of complexity: A tutorial

Bruce J. West

Publication information: REVIEWS OF MODERN PHYSICS, VOLUME Volume: 86 Published: 2014

https://www.researchgate.net/profile/Bruce_West5/publication/227146544_Fractional_Calculus_in_Bioengineering/links/555e0dc008ae9963a1140fb5.pdf

Abstract

The fractional calculus has been part of the mathematics and science literature for 310 years. However, it is only in the past decade or so that it has drawn the attention of mainstream science as a way to describe the dynamics of complex phenomena with long-term memory, spatial heterogeneity, along with nonstationary and nonergodic statistics. The most recent application encompasses complex networks, which require new ways of thinking about the world. Part of the new cognition is provided by the fractional calculus description of temporal and topological complexity. Consequently, this Colloquium is not so much a tutorial on the mathematics of the fractional calculus as it is an exploration of how complex phenomena in the physical, social, and life sciences that have eluded traditional mathematical modeling become less mysterious when certain historical assumptions such as differentiability are discarded and the ordinary calculus is replaced with the fractional calculus. Exemplars considered include the fractional differential equations describing the dynamics of viscoelastic materials, turbulence, foraging, and phase transitions in complex social networks.

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A non-local structural derivative model for characterization of ultraslow diffusion in dense colloids

LiangYingjie, ChenWen.

Publication information: Communications in Nonlinear Science and Numerical Simulation, Volume: 56 Pages: 131–137 Published: 2018

https://www.sciencedirect.com/science/article/pii/S1007570417302782

Abstract

Ultraslow diffusion has been observed in numerous complicated systems. Its mean squared displacement (MSD) is not a power law function of time, but instead a logarithmic function, and in some cases grows even more slowly than the logarithmic rate. The distributed-order fractional diffusion equation model simply does not work for the general ultraslow diffusion. Recent study has used the local structural derivative to describe ultraslow diffusion dynamics by using the inverse Mittag–Leffler function as the structural function, in which the MSD is a function of inverse Mittag–Leffler function. In this study, a new stretched logarithmic diffusion law and its underlying non-local structural derivative diffusion model are proposed to characterize the ultraslow diffusion in aging dense colloidal glass at both the short and long waiting times. It is observed that the aging dynamics of dense colloids is a class of the stretched logarithmic ultraslow diffusion processes. Compared with the power, the logarithmic, and the inverse Mittag–Leffler diffusion laws, the stretched logarithmic diffusion law has better precision in fitting the MSD of the colloidal particles at high densities. The corresponding non-local structural derivative diffusion equation manifests clear physical mechanism, and its structural function is equivalent to the first-order derivative of the MSD.

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