Open Access. Powered by Scholars. Published by Universities.®

Other Physical Sciences and Mathematics Commons

Open Access. Powered by Scholars. Published by Universities.®

280 Full-Text Articles 364 Authors 104,681 Downloads 73 Institutions

All Articles in Other Physical Sciences and Mathematics

Faceted Search

280 full-text articles. Page 9 of 11.

Expression Of Generalized Newton Iteration Method Via Generalized Local Fractional Taylor Series, Yang Xiao-Jun 2012 China University of Mining & Technology

Expression Of Generalized Newton Iteration Method Via Generalized Local Fractional Taylor Series, Yang Xiao-Jun

Xiao-Jun Yang

Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a generalized Newton iteration method derived from the generalized local fractional Taylor series with the local fractional derivatives is reviewed. Operators on real line numbers on a fractal space are induced from Cantor set to fractional set. Existence for a generalized fixed point on generalized metric spaces may take place.


Multiple Equilibrium States In A Micro-Vascular Network, David Gardner, Yiyang Li, Benjamin Small, John Geddes, Russell Carr 2012 Franklin W. Olin College of Engineering

Multiple Equilibrium States In A Micro-Vascular Network, David Gardner, Yiyang Li, Benjamin Small, John Geddes, Russell Carr

John B. Geddes

We use a simple model of micro-vascular blood flow to explore conditions that give rise to multiple equilibrium states in a three-node micro-vascular network. The model accounts for two primary rheological effects: the Fåhræus–Lindqvist effect, which describes the apparent viscosity of blood in a vessel, and the plasma skimming effect, which governs the separation of red blood cells at diverging nodes. We show that multiple equilibrium states are possible, and we use our analytical and computational tools to design an experiment for validation.


The Zero-Mass Renormalization Group Differential Equations And Limit Cycles In Non-Smooth Initial Value Problems, Yang Xiaojun 2012 China University of Mining & Technology

The Zero-Mass Renormalization Group Differential Equations And Limit Cycles In Non-Smooth Initial Value Problems, Yang Xiaojun

Xiao-Jun Yang

In the present paper, using the equation transform in fractal space, we point out the zero-mass renormalization group equations. Under limit cycles in the non-smooth initial value, we devote to the analytical technique of the local fractional Fourier series for treating zero-mass renormalization group equations, and investigate local fractional Fourier series solutions.


A Novel Approach To Processing Fractal Dynamical Systems Using The Yang-Fourier Transforms, Yang Xiaojun 2012 China University of Mining & Technology

A Novel Approach To Processing Fractal Dynamical Systems Using The Yang-Fourier Transforms, Yang Xiaojun

Xiao-Jun Yang

In the present paper, local fractional continuous non-differentiable functions in fractal space are investigated, and the control method for processing dynamic systems in fractal space are proposed using the Yang-Fourier transform based on the local fractional calculus. Two illustrative paradigms for control problems in fractal space are given to elaborate the accuracy and reliable results.


Theory And Applications Of Local Fractional Fourier Analysis, Yang Xiaojun 2012 China University of Mining & Technology

Theory And Applications Of Local Fractional Fourier Analysis, Yang Xiaojun

Xiao-Jun Yang

Local fractional Fourier analysis is a generalized Fourier analysis in fractal space. The local fractional calculus is one of useful tools to process the local fractional continuously non-differentiable functions (fractal functions). Based on the local fractional derivative and integration, the present work is devoted to the theory and applications of local fractional Fourier analysis in generalized Hilbert space. We investigate the local fractional Fourier series, the Yang-Fourier transform, the generalized Yang-Fourier transform, the discrete Yang-Fourier transform and fast Yang-Fourier transform.


Heat Transfer In Discontinuous Media, Yang Xiaojun 2012 China University of Mining & Technology

Heat Transfer In Discontinuous Media, Yang Xiaojun

Xiao-Jun Yang

From the fractal geometry point of view, the interpretations of local fractional derivative and local fractional integration are pointed out in this paper. It is devoted to heat transfer in discontinuous media derived from local fractional derivative. We investigate the Fourier law and heat conduction equation (also local fractional instantaneous heat conduct equation) in fractal orthogonal system based on cantor set, and extent them. These fractional differential equations are described in local fractional derivative sense. The results are efficiently developed in discontinuous media.


A Short Note On Local Fractional Calculus Of Function Of One Variable, Yang Xiaojun 2012 China University of Mining & Technology

A Short Note On Local Fractional Calculus Of Function Of One Variable, Yang Xiaojun

Xiao-Jun Yang

Local fractional calculus (LFC) handles everywhere continuous but nowhere differentiable functions in fractal space. This note investigates the theory of local fractional derivative and integral of function of one variable. We first introduce the theory of local fractional continuity of function and history of local fractional calculus. We then consider the basic theory of local fractional derivative and integral, containing the local fractional Rolle’s theorem, L’Hospital’s rule, mean value theorem, anti-differentiation and related theorems, integration by parts and Taylor’ theorem. Finally, we study the efficient application of local fractional derivative to local fractional extreme value of non-differentiable ...


A New Successive Approximation To Non-Homogeneous Local Fractional Volterra Equation, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiaojun 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, Yang Xiao-Jun 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.


Digital Commons powered by bepress