A New Successive Approximation To Non-Homogeneous Local Fractional Volterra Equation, 2012 China University of Mining & Technology

#### A New Successive Approximation To Non-Homogeneous Local Fractional Volterra Equation, Yang Xiaojun

*Xiao-Jun Yang*

A new successive approximation approach to the non-homogeneous local fractional Valterra equation derived from local fractional calculus is proposed in this paper. The Valterra equation is described in local fractional integral operator. The theory of local fractional derivative and integration is one of useful tools to handle the fractal and continuously non-differentiable functions, was successfully applied in engineering problem. We investigate an efficient example of handling a non-homogeneous local fractional Valterra equation.

Advanced Local Fractional Calculus And Its Applications, 2012 China University of Mining & Technology

#### Advanced Local Fractional Calculus And Its Applications, Yang Xiaojun

*Xiao-Jun Yang*

This book is the first international book to study theory and applications of local fractional calculus (LFC). It is an invitation both to the interested scientists and the engineers. It presents a thorough introduction to the recent results of local fractional calculus. It is also devoted to the application of advanced local fractional calculus on the mathematics science and engineering problems. The author focuses on multivariable local fractional calculus providing the general framework. It leads to new challenging insights and surprising correlations between fractal and fractional calculus. Keywords: Fractals - Mathematical complexity book - Local fractional calculus- Local fractional partial derivatives - Fractal ...

A Short Introduction To Yang-Laplace Transforms In Fractal Space, 2012 China University of Mining & Technology

#### A Short Introduction To Yang-Laplace Transforms In Fractal Space, Yang Xiaojun

*Xiao-Jun Yang*

The Yang-Laplace transforms [W. P. Zhong, F. Gao, In: Proc. of the 2011 3rd International Conference on Computer Technology and Development, 209-213, ASME, 2011] in fractal space is a generalization of Laplace transforms derived from the local fractional calculus. This letter presents a short introduction to Yang-Laplace transforms in fractal space. At first, we present the theory of local fractional derivative and integral of non-differential functions defined on cantor set. Then the properties and theorems for Yang-Laplace transforms are tabled, and both the initial value theorem and the final value theorem are investigated. Finally, some applications to the wave equation ...

Local Fractional Integral Equations And Their Applications, 2012 China University of Mining & Technology

#### Local Fractional Integral Equations And Their Applications, Yang Xiaojun

*Xiao-Jun Yang*

This letter outlines the local fractional integral equations carried out by the local fractional calculus (LFC). We first introduce the local fractional calculus and its fractal geometrical explanation. We then investigate the local fractional Volterra/ Fredholm integral equations, local fractional nonlinear integral equations, local fractional singular integral equations and local fractional integro-differential equations. Finally, their applications of some integral equations to handle some differential equations with local fractional derivative and local fractional integral transforms in fractal space are discussed in detail.

Local Fractional Partial Differential Equations With Fractal Boundary Problems, 2012 China University of Mining & Technology

#### Local Fractional Partial Differential Equations With Fractal Boundary Problems, Yang Xiaojun

*Xiao-Jun Yang*

This letter points out the new alternative approaches to processing local fractional partial differential equations with fractal boundary conditions. Applications of the local fractional Fourier series, the Yang-Fourier transforms and the Yang-Laplace transforms to solve of local fractional partial differential equations with fractal boundary conditions are investigated in detail.

Local Fractional Kernel Transform In Fractal Space And Its Applications, 2012 China University of Mining & Technology

#### Local Fractional Kernel Transform In Fractal Space And Its Applications, Yang Xiaojun

*Xiao-Jun Yang*

In the present paper, we point out the local fractional kernel transform based on local fractional calculus (FLC), and its applications to the Yang-Fourier transform, the Yang-Laplace transform, the local fractional Z transform, the local fractional Stieltjes transform, the local fractional volterra/ Fredholm integral equations, the local fractional volterra/ Fredholm integro-differential equations, the local fractional variational iteration algorithms, the local fractional variational iteration algorithms with an auxiliary fractal parameter, the modified local fractional variational iteration algorithms, and the modified local fractional variational iteration algorithms with an auxiliary fractal parameter.

A New Viewpoint To Fourier Analysis In Fractal Space, 2012 China University of Mining & Technology

#### A New Viewpoint To Fourier Analysis In Fractal Space, Yang Xiaojun

*Xiao-Jun Yang*

Fractional analysis is an important method for mathematics and engineering [1-21], and fractional differentiation inequalities are great mathematical topic for research [22-24]. In the present paper we point out a new viewpoint to Fourier analysis in fractal space based on the local fractional calculus [25-58], and propose the local fractional Fourier analysis. Based on the generalized Hilbert space [48, 49], we obtain the generalization of local fractional Fourier series via the local fractional calculus. An example is given to elucidate the signal process and reliable result.

Generalized Sampling Theorem For Fractal Signals, 2012 China University of Mining & Technology

#### Generalized Sampling Theorem For Fractal Signals, Yang Xiaojun

*Xiao-Jun Yang*

Local fractional calculus deals with everywhere continuous but nowhere differentiable functions in fractal space. The local fractional Fourier series is a generalization of Fourier series in fractal space, and the Yang-Fourier transform is a generalization of Fourier transform in fractal space. This letter points out the generalized sampling theorem for fractal signals (local fractional continuous signals) by using the local fractional Fourier series and Yang-Fourier transform techniques based on the local fractional calculus. This result is applied to process the local fractional continuous signals.

Picard’S Approximation Method For Solving A Class Of Local Fractional Volterra Integral Equations, 2012 China University of Mining & Technology

#### Picard’S Approximation Method For Solving A Class Of Local Fractional Volterra Integral Equations, Yang Xiaojun

*Xiao-Jun Yang*

In this letter, we fist consider the Picard’s successive approximation method for solving a class of the Volterra integral equations in local fractional integral operator sense. Special attention is devoted to the Picard’s successive approximate methodology for handling local fractional Volterra integral equations. An illustrative paradigm is shown the accuracy and reliable results.

Local Fractional Calculus And Its Applications, 2012 China University of Mining & Technology

#### Local Fractional Calculus And Its Applications, Yang Xiaojun

*Xiao-Jun Yang*

In this paper we point out the interpretations of local fractional derivative and local fractional integration from the fractal geometry point of view. From Cantor set to fractional set, local fractional derivative and local fractional integration are investigated in detail, and some applications are given to elaborate the local fractional Fourier series, the Yang-Fourier transform, the Yang-Laplace transform, the local fractional short time transform, the local fractional wavelet transform in fractal space.

Fast Yang-Fourier Transforms In Fractal Space, 2012 China University of Mining & Technology

#### Fast Yang-Fourier Transforms In Fractal Space, Yang Xiaojun

*Xiao-Jun Yang*

The Yang-Fourier transform (YFT) in fractal space is a generation of Fourier transform based on the local fractional calculus. The discrete Yang-Fourier transform (DYFT) is a specific kind of the approximation of discrete transform based on the Yang-Fourier transform in fractal space. In the present letter we point out a new fractal model for the algorithm for fast Yang-Fourier transforms of discrete Yang-Fourier transforms. It is shown that the classical fast Fourier transforms is a special example in fractal dimension a=1.

Local Fractional Fourier Analysis, 2012 China University of Mining & Technology

#### Local Fractional Fourier Analysis, Yang Xiaojun

*Xiao-Jun Yang*

Local fractional calculus (LFC) deals with everywhere continuous but nowhere differentiable functions in fractal space. In this letter we point out local fractional Fourier analysis in generalized Hilbert space. We first investigate the local fractional calculus and complex number of fractional-order based on the complex Mittag-Leffler function in fractal space. Then we study the local fractional Fourier analysis from the theory of local fractional functional analysis point of view. We finally propose the fractional-order trigonometric and complex Mittag-Leffler functions expressions of local fractional Fourier series

A Generalized Model For Yang-Fourier Transforms In Fractal Space, 2012 China University of Mining & Technology

#### A Generalized Model For Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun

*Xiao-Jun Yang*

Local fractional calculus deals with everywhere continuous but nowhere differentiable functions in fractal space. The Yang-Fourier transform based on the local fractional calculus is a generalization of Fourier transform in fractal space. In this paper, local fractional continuous non-differentiable functions in fractal space are studied, and the generalized model for the Yang-Fourier transforms derived from the local fractional calculus are introduced. A generalized model for the Yang-Fourier transforms in fractal space and some results are proposed in detail.

Generalized Local Taylor's Formula With Local Fractional Derivative, 2012 China University of Mining & Technology

#### Generalized Local Taylor's Formula With Local Fractional Derivative, Yang Xiao-Jun

*Xiao-Jun Yang*

In the present paper, a generalized local Taylor formula with the local fractional derivatives (LFDs) is proposed based on the local fractional calculus (LFC). From the fractal geometry point of view, the theory of local fractional integrals and derivatives has been dealt with fractal and continuously non-differentiable functions, and has been successfully applied in engineering problems. It points out the proof of the generalized local fractional Taylor formula, and is devoted to the applications of the generalized local fractional Taylor formula to the generalized local fractional series and the approximation of functions. Finally, it is shown that local fractional Taylor ...

Traveling Wave Solutions For The (3+1)-Dimensional Breaking Soliton Equation By (G'/G)-Expansion Method And Modiﬁed F-Expansion Method, 2012 University of Kermanshah, Razi

#### Traveling Wave Solutions For The (3+1)-Dimensional Breaking Soliton Equation By (G'/G)-Expansion Method And Modiﬁed F-Expansion Method, Mohammad Najafi M.Najafi, Mohammad Taghi Darvishi, Maliheh Najafi

*mohammad najafi*

In this paper, using (G'/G )-expansion method and modiﬁed F-expansion method, we give some explicit formulas of exact traveling wave solutions for the (3+1)-dimensional breaking soliton equation. A modiﬁed F-expansion method is proposed by taking full advantages of F-expansion method and Riccati equation in seeking exact solutions of the equation.

Ogólnotechniczne Podstawy Biotechnologii Z Elementami Grafiki Inżynierskiej Ćw., 2012 Wroclaw University of Technology

#### Ogólnotechniczne Podstawy Biotechnologii Z Elementami Grafiki Inżynierskiej Ćw., Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Materiały Odstresowujące, 2012 Wroclaw University of Technology

#### Materiały Odstresowujące, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Thermal Quench Effects On Ferroelectric Domain Walls, 2012 Universite de Geneve

#### Thermal Quench Effects On Ferroelectric Domain Walls, P. Paruch, A. B. Kolton, X. Hong, C. H. Ahn, T. Giamarchi

*Xia Hong Publications*

Using piezoresponse force microscopy on epitaxial ferroelectric thin films, we have measured the evolution of domain wall roughening as a result of heat-quench cycles up to 735 ◦C, with the effective roughness exponent ζ changing from 0.25 to 0.5. We discuss two possible mechanisms for the observed ζ increase: a quench from a thermal one-dimensional configuration and from a locally equilibrated pinned configuration with a crossover from a two- to one-dimensional regime. We find that the postquench spatial structure of the metastable states, qualitatively consistent with the existence of a growing dynamical length scale whose ultraslow evolution is ...

Assessing The Feasibility Of Cosmic-Ray Acceleration By Magnetic Turbulence At The Magnetic Center, 2012 Xavier University - Cincinnati

#### Assessing The Feasibility Of Cosmic-Ray Acceleration By Magnetic Turbulence At The Magnetic Center, M. Fatuzzo, F. Melia

*Faculty Scholarship*

No abstract provided.

Quantitative Study Of Spin-Flip Co-Tunneling Transport In A Quantum Dot, 2012 Xavier University - Cincinnati

#### Quantitative Study Of Spin-Flip Co-Tunneling Transport In A Quantum Dot, S. Herbert, T-M. Liu, A. N. Ngo

*Faculty Scholarship*

No abstract provided.