FDA Express

The ICFDA ’18 is a specialized conference on fractional-order calculus and its applications, an event of the biannual series of international conference ICFDA, http://conferences.ju.edu.jo/en/icfda2018/Lists/PastConferences/PCList.aspx.

This conference is organized under the Patronage of Her Royal Highness Princess Sumaya bint El Hassan, President of the El Hassan Science City and Royal Scientific Society, and sponsored by The University of Jordan and Scientific Research Support Fund, Jordan. Fractional Calculus is a generalization of the integer-order Calculus. The fractional-order differentiation of arbitrary orders takes into account the memory effect of many important systems. The order of the derivatives may also be variable, distributed or complex. Recently, fractional-order calculus became a more accurate tool to describe systems in various fields in mathematics, biology, chemistry, medicine, mechanics, electricity, control theory, economics, and signal and image processing. A wide range of topics on FDA are included. Prospective authors are invited to submit a full paper (4-6 pages) describing original work. All submissions should be made electronically through the conference website. Students are encouraged to participate on the best student paper award contest.

Accepted papers will be published in the conference proceedings subject to advance registration of at least one of the authors. Additionally, extended versions of selected papers will be published in special issues of international journals.

All details on committees, keynote and invited speakers, registration fees, instructions to authors, etc., can be found at the conference website.

Important Deadlines :

– Submission of tutorials and special sessions proposals: April 15, 2018;

– Submission of regular and student papers: April 15, 2018;

–Notification of acceptance: June 2, 2018;

– Submission of cameraready papers: June 25, 2018.

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Books
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The Fractional Laplacian

C. Pozrikidis

Book Description

The fractional Laplacian, also called the Riesz fractional derivative, describes an unusual diffusion process associated with random excursions. The Fractional Laplacian explores applications of the fractional Laplacian in science, engineering, and other areas where long-range interactions and conceptual or physical particle jumps resulting in an irregular diffusive or conductive flux are encountered.

* Presents the material at a level suitable for a broad audience of scientists and engineers with rudimentary background in ordinary differential equations and integral calculus

* Clarifies the concept of the fractional Laplacian for functions in one, two, three, or an arbitrary number of dimensions defined over the entire space, satisfying periodicity conditions, or restricted to a finite domain

* Covers physical and mathematical concepts as well as detailed mathematical derivations

* Develops a numerical framework for solving differential equations involving the fractional Laplacian and presents specific algorithms accompanied by numerical results in one, two, and three dimensions

* Discusses viscous flow and physical examples from scientific and engineering disciplines

Written by a prolific author well known for his contributions in fluid mechanics, biomechanics, applied mathematics, scientific computing, and computer science, the book emphasizes fundamental ideas and practical numerical computation. It includes original material and novel numerical methods.

More information on this book can be found by the following links:

https://www.crcpress.com/The-Fractional-Laplacian/Pozrikidis/p/book/9781498746151

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Fractional Calculus Applications

Roy Abi Zeid Daou ; Xavier Moreau

Book Description

After presenting the first volume of this two-volume book, presenting a lot of mathematical and theoretical studies and research related to non-integer calculus, the second volume illustrates applications related to this domain.

This volume is made up of 11 chapters. The first chapter presents the heuristic power of the non-integer differential operators in physics starting from the chaos to the emergence, the auto-organizations and the holistic rules. The second chapter shows the dynamics of the fractional order chaotic systems along with some applications. The third chapter represents the pressure control of gas engines by non-integer order controllers by showing a novel trend in the application of the fractional calculus to automotive systems. Chapter 4 shows the way to model fractional order equations using state space modeling along with some applications. Another application related to this domain is the thermal diffusive interface. Chapter 5 shows the analysis of a semi-infinite diffuse plane medium along with the equations that model this medium, and some frequency and time domain responses. However, Chapter 6 treats this problem by controlling this plant using the well-known CRONE controller. Chapter 8 presents the adaptive second-order fractional sliding mode control with an application to a water tanks level system. Chapter 9 treats the mechanical aspect by showing the features of the fractional operators applied to this domain. Also, Chapter Nine presents the theory of diffusive stresses based on the fractional advection-diffusion equation. The modeling of drug diffusion during general anesthesia using Fractional Calculus is shown in Chapter 10 and is considered as another application related to the biomedical field. Finally, Chapter 11 represents an overview of the fractional fuzzy controllers by showing the analysis, the synthesis and the implementation of this module.

To sum up, this second volume presents applications of fractional calculus in several engineering domains as the thermal, the automotive, the mechanical, the biomedical and much more. Note that this volume was preceded by a first volume that focuses on the mathematical and theoretical aspects of fractional calculus. (Imprint: Nova)

More information on this book can be found by the following links:

https://www.novapublishers.com/catalog/product_info.php?products_id=51947

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Journals
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Annals of Physics

(selected)

The fractional dynamics of quantum systems

Longzhao Lu, Xiangyang Yu

Fractional Ornstein–Uhlenbeck noise

Kwok Sau Fa

Time-dependent fractional dynamics with memory in quantum and economic physics

Vasily E. Tarasov, Valentina V. Tarasova

Fractional corresponding operator in quantum mechanics and applications: A uniform fractional Schrödinger equation in form and fractional quantization methods

Xiao Zhang, Chaozhen Wei, Yingming Liu, Maokang Luo

Quantum spin chains with fractional revival

Vincent X. Genest, Luc Vinet, Alexei Zhedanov

Accessible solitons of fractional dimension

Wei-Ping Zhong, Milivoj Belić, Yiqi Zhang

Fractional power-law spatial dispersion in electrodynamics

Vasily E. Tarasov, Juan J. Trujillo

Fractional vector calculus and fractional Maxwell’s equations

Vasily E. Tarasov

A physically based connection between fractional calculus and fractal geometry

Salvatore Butera, Mario Di Paola

Fractional hydrodynamic equations for fractal media

Vasily E. Tarasov

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Systems & Control Letters

(Selected)

Parameters and fractional differentiation orders estimation for linear continuous-time non-commensurate fractional order systems

Zehor Belkhatir, Taous Meriem Laleg-Kirati

Quadratic Lyapunov functions for stability analysis in fractional-order systems with not necessarily differentiable solutions

Aldo-Jonathan Muñoz-Vázquez, Vicente Parra-Vega, Anand Sánchez-Orta, Gerardo Romero-Galván

Constrained controllability of fractional linear systems with delays in control

Beata Sikora, Jerzy Klamka

Necessary and sufficient conditions of observer-based stabilization for a class of fractional-order descriptor systems

Chong Lin, Bing Chen, Peng Shi, Jin-Peng Yu

Robust stability of fractional order system with general interval uncertainties

Shiqi Zheng

Exact stability test and stabilization for fractional systems

J.Y. Kaminski, R. Shorten, E. Zeheb

A fractional representation approach to the robust regulation problem for SISO systems

P. Laakkonen, A. Quadrat

BIBO stability of some classes of delay systems and fractional systems

Aolo Bashar Abusaksaka, Jonathan R. Partington

A stability test for non-commensurate fractional order systems

Jocelyn Sabatier, Christophe Farges, Jean-Claude Trigeassou

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Paper Highlight
A physically based connection between fractional calculus and fractal geometry

Butera, Salvatore; Di Paola, Mario

Publication information: ANNALS OF PHYSICS Volume: 350 Pages: 146-158 Published: NOV 2014

https://www.sciencedirect.com/science/article/pii/S0003491614001791

Abstract

We show a relation between fractional calculus and fractals, based only on physical and geometrical considerations. The link has been found in the physical origins of the power-laws, ruling the evolution of many natural phenomena, whose long memory and hereditary properties are mathematically modelled by differential operators of non integer order. Dealing with the relevant example of a viscous fluid seeping through a fractal shaped porous medium, we show that, once a physical phenomenon or process takes place on an underlying fractal geometry, then a power-law naturally comes up in ruling its evolution, whose order is related to the anomalous dimension of such geometry, as well as to the model used to describe the physics involved. By linearizing the non linear dependence of the response of the system at hand to a proper forcing action then, exploiting the Boltzmann superposition principle, a fractional differential equation is found, describing the dynamics of the system itself. The order of such equation is again related to the anomalous dimension of the underlying geometry.

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Connecting complexity with spectral entropy using the Laplace transformed solution to the fractional diffusion equation

Liang, Yingjie; Chen, Wen; Magin, Richard L.

Publication information: PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS Volume: 453 Pages: 327-335 Published: JUL 1 2016

http://www.sciencedirect.com/science/article/pii/S0378437116002223

Abstract

Analytical solutions to the fractional diffusion equation are often obtained by using Laplace and Fourier transforms, which conveniently encode the order of the time and the space derivatives (alpha and beta) as non-integer powers of the conjugate transform variables (s, and k) for the spectral and the spatial frequencies, respectively. This study presents a new solution to the fractional diffusion equation obtained using the Laplace transform and expressed as a Fox's H-function. This result clearly illustrates the kinetics of the underlying stochastic process in terms of the Laplace spectral frequency and entropy. The spectral entropy is numerically calculated by using the direct integration method and the adaptive Gauss-Kronrod quadrature algorithm. Here, the properties of spectral entropy are investigated for the cases of sub-diffusion and super-diffusion. We find that the overall spectral entropy decreases with the increasing alpha and beta, and that the normal or Gaussian case with alpha = 1 and beta = 2, has the lowest spectral entropy (i.e., less information is needed to describe the state of a Gaussian process). In addition, as the neighborhood over which the entropy is calculated increases, the spectral entropy decreases, which implies a spatial averaging or coarse graining of the material properties. Consequently, the spectral entropy is shown to provide a new way to characterize the temporal correlation of anomalous diffusion. Future studies should be designed to examine changes of spectral entropy in physical, chemical and biological systems undergoing phase changes, chemical reactions and tissue regeneration.

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