FDA Express

Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 19 Issue: 4 Pages: 821-829 DOI: 10.1016/j.cnsns.2013.07.025 Published: APR 2014

Title: Analysis of temperature time-series: Embedding dynamics into the MDS method

Author(s): Lopes, Antonio M.; Tenreiro Machado, J. A.

Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 19 Issue: 4 Pages: 851-871 DOI: 10.1016/j.cnsns.2013.08.031 Published: APR 2014

Title: POSITIVE SOLUTIONS OF NONHOMOGENEOUS FRACTIONAL LAPLACIAN PROBLEM WITH CRITICAL EXPONENT

Author(s): Shang, Xudong; Zhang, Jihui; Yang, Yang

Source: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume: 13 Issue: 2 Pages: 567-584 DOI: 10.3934/cpaa.2014.13.567 Published: MAR 2014

Title: WELL-POSEDNESS OF ABSTRACT DISTRIBUTED-ORDER FRACTIONAL DIFFUSION EQUATIONS

Author(s): Jia, Junxiong; Peng, Jigen; Li, Kexue

Source: COMMUNICATIONS ON PURE AND APPLIED ANALYSIS Volume: 13 Issue: 2 Pages: 605-621 DOI: 10.3934/cpaa.2014.13.605 Published: MAR 2014

Title: Comments on the concept of existence of solution for impulsive fractional differential equations

Author(s): Wang, Guotao; Ahmad, Bashir; Zhang, Lihong; et al.

Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION Volume: 19 Issue: 3 Pages: 401-403 DOI: 10.1016/j.cnsns.2013.04.003 Published: MAR 2014

[Back]

==========================================================================

Books

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

The Human Respiratory System ---- An Analysis of the Interplay between Anatomy, Structure, Breathing and Fractal Dynamics

Clara Mihaela Ionescu

Book Description

The objective of the book is to put forward emerging ideas from biology and mathematics into biomedical engineering applications in general with special attention to the analysis of the human respiratory system. The field of fractional calculus is mature in mathematics and chemistry, but still in infancy in engineering applications. However, the last two decades have been very fruitful in producing new ideas and concepts with applications in biomedical engineering. The reader should find the book a revelation of the latest trends in modeling and identification of the human respiratory parameters for the purpose of diagnostic and monitoring. Of special interest here is the notion of fractal structure, which tells us something about the biological efficiency of the human respiratory system. Related to this notion is the fractal dimension, relating the adaptation of the fractal structure to environmental changes (i.e. disease). Finally, we have the dynamical pattern of breathing, which is then the result of both the structure and the adaptability of the respiratory system.

The distinctive feature of the book is that it offers a bottom-up approach, starting from the basic anatomical structure of the respiratory system and continuing with the dynamic pattern of the breathing. The relations between structure (or the specific changes within it) and fundamental working of the system as a whole are pinned such that the reader can understand their interplay. Moreover, this interplay becomes crucial when alterations at the structural level in the airway caused by disease may require adaptation of the body to the functional requirements of breathing (i.e. to ensure the necessary amount of oxygen to the organs). Adaptation of the human body, and specially of the respiratory system, to various conditions can be thus explained and justified in terms of breathing efficiency.

The motivation for putting together this book is to give by means of the example chosen (i.e. the respiratory system) an impulse to the engineering and medical community in embracing these new ideas and becoming aware of the interaction between these disciplines. The net benefit of reading this book is the advantage of any researcher who wants to stay up to date with the new emerging research trends in biomedical applications. The book offers the reader an opportunity to become aware of a novel, unexplored, and yet challenging research direction.

More information on this book can be found by the following link: http://link.springer.com/book/10.1007/978-1-4471-5388-7

[Back]

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Fractional Calculus: An Introduction for Physicists (2nd Edition)

Richard Herrmann

Book Description

The book presents a concise introduction to the basic methods and strategies in fractional calculus and enables the reader to catch up with the state of the art in this field as well as to participate and contribute in the development of this exciting research area. The contents are devoted to the application of fractional calculus to physical problems. The fractional concept is applied to subjects in classical mechanics, group theory, quantum mechanics, nuclear physics, hadron spectroscopy and quantum field theory and it will surprise the reader with new intriguing insights. This new, extended edition now also covers additional chapters about image processing, folded potentials in cluster physics, infrared spectroscopy and local aspects of fractional calculus. A new feature is exercises with elaborated solutions, which significantly supports a deeper understanding of general aspects of the theory. As a result, this book should also be useful as a supporting medium for teachers and courses devoted to this subject.

More information on this book can be found by the following link: http://www.gigahedron.de/wpgh/fractional-calculus-introduction-for-physicists-2nd-edition/

[Back]

========================================================================

Journals

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Fractional Calculus and Applied Analysis

Volume 16, Issue 4

Virginia Kiryakova, John J. O’Connor

A characteristic of fractional resolvents

Zhan-Dong Mei, Ji-Gen Peng, Yang Zhang

Controllability of fractional order system with nonlinear term having integral contractor

Surendra Kumar, Nagarajan Sukavanam

Two equivalent Stefan’s problems for the time fractional diffusion equation

Sabrina Roscani, Eduardo Santillan Marcus

Existence results for nonlinear quadratic integral equations of fractional order in Banach algebra

Ahmed El-Sayed, Hind Hashem

The fractional Laplacian as a limiting case of a self-similar spring model and applications to n-dimensional anomalous diffusion

Thomas M. Michelitsch, Gérard A. Maugin

Fractional-hyperbolic systems

Anatoly N. Kochubei

Nonpolynomial collocation approximation of solutions to fractional differential equations

Neville J. Ford, M. Luísa Morgado, Magda Rebelo

A new difference scheme for time fractional heat equations based on the Crank-Nicholson method

Ibrahim Karatay, Nurdane Kale

New relationships connecting a class of fractal objects and fractional integrals in space

Raoul R. Nigmatullin, Dumitru Baleanu

Unique positive solution for a fractional boundary value problem

Keyu Zhang, Jiafa Xu

Fractional derivatives of multidimensional Colombeau generalized stochastic processes

Danijela Rajter-Ćirić, Mirjana Stojanović

Application of measure of noncompactness to a Cauchy problem for fractional differential equations in Banach spaces

Asadollah Aghajani, Ehsan Pourhadi

A Lyapunov-type inequality for a fractional boundary value problem

Rui A. C. Ferreira

Positive solutions for a system of nonlocal fractional boundary value problems

Johnny Henderson, Rodica Luca

[Back]

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Computers & Mathematics with Applications

Volume 66, Issue 12

Local method of approximate particular solutions for two-dimensional unsteady Burgers’ equations

Xueying Zhang, Haiyan Tian, Wen Chen

A generalization of the optimal diagonal approximate inverse preconditioner

Luis González, Antonio Suárez, Eduardo Rodríguez

Block conjugate gradient type methods for the approximation of bilinear form

Lei Du, Yasunori Futamura, Tetsuya Sakurai

An a posteriori error estimator for an unsteady advection–diffusion–reaction problem

Rodolfo Araya, Pablo Venegas

Integral equation formulation of an unsteady diffusion–convection equation with variable coefficient and velocity

J. Ravnik, L. Škerget

An efficient hybrid BEM–RBIE method for solving conjugate heat transfer problems

Ean Hin Ooi, Viktor Popov

Estimation of computational homogenization error by explicit residual method

M. Oleksy, W. Cecot

Adaptive optimal control approximation for solving a fourth-order elliptic variational inequality

Weidong Cao, Danping Yang

Multiplicity of solutions for a class of quasilinear Schrödinger systems in

Dengfeng Lü, Qiong Liu

On the natural stabilization of convection dominated problems using high order Bubnov–Galerkin finite elements

Q. Cai, S. Kollmannsberger, E. Sala-Lardies, A. Huerta, E. Rank

Multi-soliton and double Wronskian solutions of a ()-dimensional modified Heisenberg ferromagnetic system

Gao-Qing Meng, Yi-Tian Gao, Yu-Hao Sun, Yi Qin, Xin Yu

Analysis of the discontinuous Petrov–Galerkin method with optimal test functions for the Reissner–Mindlin plate bending model

Victor M. Calo, Nathaniel O. Collier, Antti H. Niemi

On new existence results for fractional integro-differential equations with impulsive and integral conditions

A. Anguraj, P. Karthikeyan, M. Rivero, J.J. Trujillo

Comments on “Sufficiency and duality for multiobjective variational control problems with -invexity” Computers and Mathematics with Applications 63, 838–850 (2012)

Tadeusz Antczak

[Back]

==========================================================================

Paper Highlight

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Fractional order differential equations on an unbounded domain

A. Arara, M. Benchohra, N. Hamidi, J.J. Nieto

Publication information: A. Arara, M. Benchohra, N. Hamidi, J.J. Nieto. Fractional order differential equations on an unbounded domain. Nonlinear Analysis: Theory, Methods & Applications 72(2), 2010, 580–586.
http://www.sciencedirect.com/science/article/pii/S0362546X09008670

Abstract
We are concerned with the existence of bounded solutions of a boundary value problem on an unbounded domain for differential equations involving the Caputo fractional derivative. Our results are based on a fixed point theorem of Schauder combined with the diagonalization method.
　

[Back]

－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－－

Fractional diffusion equation with a generalized Riemann–Liouville time fractional derivative

Trifce Sandev, Ralf Metzler and Živorad Tomovski

Publication information: Trifce Sandev, Ralf Metzler and Živorad Tomovski. Fractional diffusion equation with a generalized Riemann–Liouville time fractional derivative. J. Phys. A: Math. Theor. 44, 2011, 255203 doi:10.1088/1751-8113/44/25/255203
http://iopscience.iop.org/1751-8121/44/25/255203

Abstract
In this paper, the solution of a fractional diffusion equation with a Hilfer-generalized Riemann–Liouville time fractional derivative is obtained in terms of Mittag–Leffler-type functions and Fox's H-function. The considered equation represents a quite general extension of the classical diffusion (heat conduction) equation. The methods of separation of variables, Laplace transform, and analysis of the Sturm–Liouville problem are used to solve the fractional diffusion equation defined in a bounded domain. By using the Fourier–Laplace transform method, it is shown that the fundamental solution of the fractional diffusion equation with a generalized Riemann–Liouville time fractional derivative defined in the infinite domain can be expressed via Fox's H-function. It is shown that the corresponding solutions of the diffusion equations with time fractional derivative in the Caputo and Riemann–Liouville sense are special cases of those diffusion equations with the Hilfer-generalized Riemann–Liouville time fractional derivative. The asymptotic behaviour of the solutions are found for large values of the spatial variable. The fractional moments of the fundamental solution of the fractional diffusion equation are obtained. The obtained results are relevant in the context of glass relaxation and aquifer problems.

[Back]

==========================================================================

The End of This Issue

∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽∽