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- Journal articles (19)
- Fractal space (3)
- Variational iteration method (3)
- Articles (Local Journals) (2)
- Fractal (2)
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- Informacje dla studentów (in Polish) (2)
- Local fractional Fourier series (2)
- Local fractional derivative (2)
- Yang-Fourier transforms (2)
- (G'/G)-expansion method (1)
- (G'/G)-expansion method or F-expansion method (1)
- Adomian decomposition method (1)
- Ancient Chinese mathematics (1)
- Approximation; Non-homogeneous local fractional Valterra equation; Local fractional operator; local fractional calculus (1)
- Boundary element method (1)
- Clebsch potentials (1)
- Compacton (1)
- Computerized symbolic computation (1)
- Discontinuous system (1)
- Discrete (1)
- EHTA Method (1)
- Exact solution (1)
- Exp-function method (1)
- F-expansion method (1)
- FIM methods (1)
- Fast reversible reaction (1)
- Fermat's principle (1)
- First-order chemical reaction (1)
- Fourier analysis (1)
- Fractal boundary conditions (1)
Articles 1 - 30 of 43
Full-Text Articles in Physical Sciences and Mathematics
Numerical Solution Of A Reaction-Diffusion System With Fast Reversible Reaction By Using Adomian’S Decomposition Method And He’S Variational Iteration Method, Ann J. Al-Sawoor Ph.D., Mohammed O. Al-Amr M.Sc.
Numerical Solution Of A Reaction-Diffusion System With Fast Reversible Reaction By Using Adomian’S Decomposition Method And He’S Variational Iteration Method, Ann J. Al-Sawoor Ph.D., Mohammed O. Al-Amr M.Sc.
Mohammed O. Al-Amr
In this paper, the approximate solution of a reaction-diffusion system with fast reversible reaction is obtained by using Adomian decomposition method (ADM) and variational iteration method (VIM) which are two powerful methods that were recently developed. The VIM requires the evaluation of the Lagrange multiplier, whereas ADM requires the evaluation of the Adomian polynomials. The behavior of the approximate solutions and the effects of different values of t are shown graphically.
Local Fractional Fourier Series With Application To Wave Equation In Fractal Vibrating String, Yang Xiaojun
Local Fractional Fourier Series With Application To Wave Equation In Fractal Vibrating String, Yang Xiaojun
Xiao-Jun Yang
We introduce the wave equation in fractal vibrating string in the framework of the local fractional calculus. Our particular attention is devoted to the technique of the local fractional Fourier series for processing these local fractional differential operators in a way accessible to applied scientists. By applying this technique we derive the local fractional Fourier series solution of the local fractional wave equation in fractal vibrating string and show the fundamental role of the Mittag- Leffler function.
The Block Aor Iterative Methods For Solving Fuzzy Linear Systems, Hs Najafi, Sa Edalatpanah
The Block Aor Iterative Methods For Solving Fuzzy Linear Systems, Hs Najafi, Sa Edalatpanah
SA Edalatpanah
In this article the block AOR Iterative methods are used for solving fuzzy linear systems. The convergence of the methods and functional relationship between eigenvalues in block AOR is investigated.
Variational Iteration Method For Q-Difference Equations Of Second Order, Guo-Cheng Wu
Variational Iteration Method For Q-Difference Equations Of Second Order, Guo-Cheng Wu
G.C. Wu
Recently, Liu extended He's variational iteration method to strongly nonlinear q-difference equations. In this study, the iteration formula and the Lagrange multiplier are given in a more accurate way. The q-oscillation equation of second order is approximately solved to show the new Lagrange multiplier's validness.
The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun
The Discrete Yang-Fourier Transforms In Fractal Space, Yang Xiao-Jun
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, used in Yang-Fourier transform in fractal space. This paper points out new standard forms of discrete Yang-Fourier transforms (DYFT) of fractal signals, and both properties and theorems are investigated in detail.
Expression Of Generalized Newton Iteration Method Via Generalized Local Fractional Taylor Series, Yang Xiao-Jun
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.
Preconditioning Strategy To Solve Fuzzy Linear Systems (Fls), Sa Edalatpanah
Preconditioning Strategy To Solve Fuzzy Linear Systems (Fls), Sa Edalatpanah
SA Edalatpanah
In this article, the preconditioning methods are used for fuzzy linear systems and especially some new preconditioners are introduced. Moreover, the preconditioned iterative methods are studied from the point of view of rate of convergence and the convergence properties of the proposed methods have been analyzed and compared with the classical methods. Finally, the methods are tested by numerical example that shows a good improvement on the convergence speed.
The Zero-Mass Renormalization Group Differential Equations And Limit Cycles In Non-Smooth Initial Value Problems, Yang Xiaojun
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.
Some Approaches For Using Stationary Iterative Methods To Linear Equations Generated From The Boundary Element Method, Hs Najafi, Sa Edalatpanah, B Parsa Moghaddam
Some Approaches For Using Stationary Iterative Methods To Linear Equations Generated From The Boundary Element Method, Hs Najafi, Sa Edalatpanah, B Parsa Moghaddam
SA Edalatpanah
For linear equations, there are numerous stationary iterative methods. However, these methods are not applicable in some important problems such as linear system arising from the boundary element method (BEM). In this paper, we proposed two approaches for using stationary iterative methods to linear equations arising from the BEM for the Laplace and convective diffusion with first-order chemical reaction problems. Our proposed methods are simple and graceful. Finally, numerical example is given to show the efficiency of our results.
A Kind Of Symmetrical Iterative Methods To Solve Special Class Of Lcp (M, Q), Sa Edalatpanah, Hs Najafi
A Kind Of Symmetrical Iterative Methods To Solve Special Class Of Lcp (M, Q), Sa Edalatpanah, Hs Najafi
SA Edalatpanah
No abstract provided.
Nash Equilibrium Solution Of Fuzzy Matrix Game Solution Of Fuzzy Bimatrix Game, Sa Edalatpanah, Hs Najafi
Nash Equilibrium Solution Of Fuzzy Matrix Game Solution Of Fuzzy Bimatrix Game, Sa Edalatpanah, Hs Najafi
SA Edalatpanah
In this paper, we propose a method for finding Nash equilibrium of fuzzy games. This method is based on ranking function of fuzzy linear programming which simplifies the solving process of fuzzy Nash equilibrium. Numerical results show that the proposed method is competitive to the state-of-the-art algorithms.
A New Two-Phase Method For The Fuzzy Primal Simplex Algorithm, Sa Edalatpanah, S Shahabi
A New Two-Phase Method For The Fuzzy Primal Simplex Algorithm, Sa Edalatpanah, S Shahabi
SA Edalatpanah
Recently, Nasseri et al., [1, 2] proposed fuzzy two-phase method involving fuzzy artificial variables and fuzzy big-M method to obtain an initial fuzzy basic feasible solution to solve the linear programming with fuzzy variables (FVLP) problems. In this paper, we propose a new two-phase method for solving fuzzy linear programming. Our method needs not any artificial variables and has an advantage of the simple implementation. Furthermore this method is more effective and faster than above methods.
New Model For Preconditioning Techniques With Application To The Boundary Value Problems, Sa Edalatpanah, Hs Najafi
New Model For Preconditioning Techniques With Application To The Boundary Value Problems, Sa Edalatpanah, Hs Najafi
SA Edalatpanah
No abstract provided.
A Novel Approach To Processing Fractal Dynamical Systems Using The Yang-Fourier Transforms, Yang Xiaojun
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.
Interpolation Of Fuzzy Data By Using Quadratic Piecewise Polynomial Induced Form E(3) Cubic Splines, H. Behforooz, R. Ezzati, Saeid Abbasbandy
Interpolation Of Fuzzy Data By Using Quadratic Piecewise Polynomial Induced Form E(3) Cubic Splines, H. Behforooz, R. Ezzati, Saeid Abbasbandy
Saeid Abbasbandy
In this paper, we will consider the interpolation of fuzzy data by using the fuzzy-valued piecewise quartic polynomials Qy0,y1,..., yn (x) induced from E(3) cubic spline functions.
Effective Calculation Of Multiple Solutions Of Mixed Convection In A Porous Medium, Saeid Abbasbandy, E. Shivanian
Effective Calculation Of Multiple Solutions Of Mixed Convection In A Porous Medium, Saeid Abbasbandy, E. Shivanian
Saeid Abbasbandy
This paper considers an important model of boundary value problem with a condition at infinity namely combined free and forced convection over a plane of arbitrary shape embedded in a fluid-saturated porous medium; this model admits dual solutions, and uses a technique, which is to some extent modification of homotopy analysis method (HAM), in order to obtain dual solutions analytically with high accuracy.
Converting Fractional Differential Equations Into Partial Differential Equations, Ji-Huan He, Zheng-Biao Li
Converting Fractional Differential Equations Into Partial Differential Equations, Ji-Huan He, Zheng-Biao Li
Ji-Huan He
A transform is suggested in this paper to convert fractional differential equations with the modified Riemann-Liouville derivative into partial differential equations, and it is concluded that the fractional order in fractional differential equations is equivalent to the fractal dimension.
Asymptotic Methods For Solitary Solutions And Compactons, Ji-Huan He
Asymptotic Methods For Solitary Solutions And Compactons, Ji-Huan He
Ji-Huan He
This review is an elementary introduction to some new asymptotic methods for the search for the solitary solutions of nonlinear differential equations, nonlinear differential-difference equations, and nonlinear fractional differential equations . Particular attention is paid throughout the paper to giving an intuitive grasp for the variational approach, the Hamiltonian approach, the variational iteration method, the homotopy perturbation method, the parameter-expansion method, the Yang-Laplace Transform, the Yang-Fourier transform, and ancient Chinese mathematics. Hamilton principle and variational principles are also emphasized. The reviewed asymptotic methods are easy to be followed for various applications. Some ideas on this review article are first appeared. …
Theory And Applications Of Local Fractional Fourier Analysis, Yang Xiaojun
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
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
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 functions, and give …
A New Successive Approximation To Non-Homogeneous Local Fractional Volterra Equation, Yang Xiaojun
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
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 …
A Short Introduction To Yang-Laplace Transforms In Fractal Space, Yang Xiaojun
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
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
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
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
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
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
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.