FDA Express

This short monograph is a spin-off of the author’s “Fractional Differentiation Inequalities,” a research monograph published by Springer, New York, 2009. It continues and complements the earlier book to various interesting and important directions.

Fractional differentiation inequalities are by themselves an important and great mathematical topic for research. Furthermore they have many applications, the most important ones are in establishing uniqueness of solution in fractional differential equations and systems and in fractional partial differential equations. Also they provide upper bounds to the solutions of the above equations.

More information on this book can be found by the following link: http://link.springer.com/book/10.1007/978-0-387-98128-4

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New Trends in Nanotechnology and Fractional Calculus Applications

Dumitru Baleanu, Ziya B. Guvenc, J. A. Tenreiro Machado

Book Description

This book contains some of the contributions that were presented at NTST08 and FDA08 and, after being carefully selected and peer-reviewed, were expanded and grouped into ﬁve main sections entitled “New Trends in Nanotechnology”,“Techniques and Applications”, “Mathematical Tools”, “Fractional Modelling” and “Fractional Control Systems”. The selection of improved papers for publication in this book reflects the success of the workshops, with the emergence of a variety of novel areas of applications. Bearing these ideas in mind the guest editorswould like to honor many distinguished scientists that have promoted the development of nanoscience and fractional calculus and, in particular, Prof. George M. Zaslavsky that supported early this special issue and passed away recently. 　

More information on this book can be found by the following link: http://link.springer.com/book/10.1007/978-90-481-3293-5

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Journals

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Chaos, Solitons & Fractals

Volume 68, Pages 1-186 (Selected)

Risk assessment for infectious disease and its impact on voluntary vaccination behavior in social networks

Eriko Fukuda, Satoshi Kokubo, Jun Tanimoto, Zhen Wang, Aya Hagishima, Naoki Ikegaya

Exact soliton solutions to a new coupled integrable short light-pulse system

Hermann T. Tchokouansi, Victor K. Kuetche, Timoleon C. Kofane

Limit cycle bifurcations in a class of near-Hamiltonian systems with multiple parameters

Maoan Han, Yanqin Xiong

Endogenous fields enhanced stochastic resonance in a randomly coupled neuronal network

Bin Deng, Lin Wang, Jiang Wang, Xi-le Wei, Hai-tao Yu

The moment Lyapunov exponent for a three-dimensional stochastic system

Xuan Li, Xianbin Liu

Conjugate coupling in ecosystems: Cross-predation stabilizes food webs

Rajat Karnatak, Ram Ramaswamy, Ulrike Feudel

Cooperation of deterministic and stochastic mechanisms resulting in the intermittent behavior

Olga I. Moskalenko, Alexey A. Koronovskii, Alexander E. Hramov, Maxim O. Zhuravlev, Yurij I. Levin

Quantification of synchronization phenomena in two reciprocally gap-junction coupled bursting pancreatic β-cells

Jing Wang, Shenquan Liu, Xuanliang Liu

Traffic dynamics on coupled spatial networks

Wen-Bo Du, Xing-Lian Zhou, Zhen Chen, Kai-Quan Cai, Xian-Bin Cao

Analysis of effect of random perturbation on dynamic response of gear transmission system

Jingyue Wang, Haotian Wang, Lixin Guo

Short-term prediction method of wind speed series based on fractal interpolation

Chunbo Xiu, Tiantian Wang, Meng Tian, Yanqing Li, Yi Cheng

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Fractional Calculus and Applied Analysis

Volume 17, Issue 4, December（selected）

Nonclassical convolutions and their uses

Ivan H. Dimovski

A theorem of uniqueness of the solution of nonlocal evolution boundary value problem

Yulian Tsankov

Viscoelastic flows with fractional derivative models: Computational approach by convolutional calculus of Dimovski

Emilia Bazhlekova, Ivan Bazhlekov

From the hyper-Bessel operators of Dimovski to the generalized fractional calculus

Virginia Kiryakova

A family of hyper-Bessel functions and convergent series in them

Jordanka Paneva-Konovska

Multiple solutions to boundary value problem for impulsive fractional differential equations

Rosana Rodríguez-López, Stepan Tersian

Extending the Stieltjes transform II

Dennis Nemzer

Nonstandard Gauss—Lobatto quadrature approximation to fractional derivatives

Shahrokh Esmaeili, Gradimir V. Milovanović

Asymptotic estimates of solutions to initial-boundary-value problems for distributed order time-fractional diffusion equations

Zhiyuan Li, Yuri Luchko, Masahiro Yamamoto

Existence results of mild solutions for impulsive fractional integro-differential evolution equations with infinite delay

Shengli Xie

Reflection symmetric Erdélyi-Kober type operators — A quasi-particle interpretation

Richard Herrmann

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Paper Highlight
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Expansion formula for fractional derivatives in variational problems

Teodor M. Atanacković, Marko Janev, Sanja Konjik, Stevan Pilipović, Dušan Zorica

Publication information: Teodor M. Atanacković, Marko Janev, Sanja Konjik, Stevan Pilipović, Dušan Zorica, Expansion formula for fractional derivatives in variational problems, Journal of Mathematical Analysis and Applications 409, 2, 2014, Pages 911-924.

http://www.sciencedirect.com/science/article/pii/S0022247X13007191

Abstract

We modify the expansion formula introduced in [T.M. Atanacković, B. Stanković, An expansion formula for fractional derivatives and its applications, Fract. Calc. Appl. Anal. 7 (3) (2004) 365–378] for the left Riemann–Liouville fractional derivative in order to apply it to various problems involving fractional derivatives. As a result we obtain a new form of the fractional integration by parts formula, with the benefit of a useful approximation for the right Riemann–Liouville fractional derivative, and derive a consequence of the fractional integral inequality. Further, we use this expansion formula to transform fractional optimization (minimization of a functional involving fractional derivatives) to the standard constrained optimization problem. It is shown that when the number of terms in the approximation tends to infinity, solutions to the Euler–Lagrange equations of the transformed problem converge, in a weak sense, to solutions of the original fractional Euler–Lagrange equations. An illustrative example is treated numerically.

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Stationary response of Duffing oscillator with hardening stiffness and fractional derivative

Lincong Chen, Weihua Wang, Zhongshen Li, Weiqiu Zhu

Publication information: Lincong Chen, Weihua Wang, Zhongshen Li, Weiqiu Zhu, Stationary response of Duffing oscillator with hardening stiffness and fractional derivative, International Journal of Non-Linear Mechanics, 48, 2013, Pages 44–50.

http://www.sciencedirect.com/science/article/pii/S0020746212001229

Abstract

The stationary response of Duffing oscillator with hardening stiffness and fractional derivative under Gaussian white noise excitation is studied. First, the term associated with fractional derivative is separated into the equivalent quasi-linear dissipative force and quasi-linear restoring force by using the generalized harmonic balance technique, and the original system is replaced by an equivalent nonlinear stochastic system without fractional derivative. Then, the stochastic averaging method of energy envelope is applied to the equivalent nonlinear stochastic system to yield the averaged Itô equation of energy envelope, from which the corresponding Fokker–Planck–Kolmogorov (FPK) equation is established and solved to obtain the stationary probability densities of the energy envelope and the amplitude envelope. The accuracy of the analytical results is validated by those from the Monte Carlo simulation of original system.

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The End of This Issue

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