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Physical Sciences and Mathematics Commons™
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- ISI journals (9)
- Journal articles (2)
- Published Articles (2)
- Articles (Local Journals) (1)
- CO2 separation (1)
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- Carbonic anhydrase (1)
- Consistent scheme (1)
- Convergence theorem; single splitting; double splitting; iterative methods; spectral radius. (1)
- Discrete Adomian decomposition method (1)
- Finite difference scheme (1)
- Finite element scheme (1)
- Fractal medium (1)
- Fractional analysis (1)
- Fredholm integral equation; System of integral equations; Legendre multi- wavelets; Collocation method; Multiresolution of analysis (MRA); Algebraic equations. (1)
- Generalized Banach space (1)
- Generalized Burger’s–Huxley equation (1)
- Heat-conduction (1)
- Informacje dla studentów (in Polish) (1)
- Local fractional Fourier series method (1)
- Local fractional differential equation (1)
- Local fractional functional analysis (1)
- Lumped scheme. (1)
- Nonlinear time-delay system; Constrained optimal control; Control parameterization; Improved differential evolution; Fed-batch fermentation (1)
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- Prace ze studentami (in Polish) (1)
- Reaction-diffusion system (1)
- Variational Iteration Method (Fractional Calculus) (1)
Articles 1 - 19 of 19
Full-Text Articles in Physical Sciences and Mathematics
Variational Iteration Method For The Burgers' Flow With Fractional Derivatives—New Lagrange Multipliers, Guo-Cheng Wu, Dumitru Baleanu
Variational Iteration Method For The Burgers' Flow With Fractional Derivatives—New Lagrange Multipliers, Guo-Cheng Wu, Dumitru Baleanu
G.C. Wu
The flow through porous media can be better described by fractional models than the classical ones since they include inherently memory effects caused by obstacles in the structures. The variational iteration method was extended to find approximate solutions of fractional differential equations with the Caputo derivatives, but the Lagrange multipliers of the method were not identified explicitly. In this paper, the Lagrange multiplier is determined in a more accurate way and some new variational iteration formulae are presented.
Application Of The Local Fractional Series Expansion Method And The Variational Iteration Method To The Helmholtz Equation Involving Local Fractional Derivative Operators, Yang Xiaojun
Xiao-Jun Yang
We investigate solutions of the Helmholtz equation involving local fractional derivative operators. We make use of the series expansion method and the variational iteration method, which are based upon the local fractional derivative operators. The nondifferentiable solution of the problem is obtained by using these methods.
Optimal Control For A Nonlinear Time-Delay System In Fed-Batch Fermentation, Chongyang Liu, Zhaohua Gong, Enmin Feng
Optimal Control For A Nonlinear Time-Delay System In Fed-Batch Fermentation, Chongyang Liu, Zhaohua Gong, Enmin Feng
Chongyang Liu
The main control goal in fed-batch fermentation is to maximize yield of target product and reduce operation costs. In this paper, we propose a controlled nonlinear time-delay system, in which the flow rate of glycerol is taken as the control function and the terminal time of the fermentation as the optimization variable, to model the 1,3-propanediol (1,3-PD) production in fed-batch process. Taking the mass of 1,3-PD per unit time as the performance index, we formulate a constrained optimal control model with free terminal time to optimize the production process. Using a time-scale transformation, the optimal control problem is equivalently transcribed …
Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators, Yang Xiaojun
Mappings For Special Functions On Cantor Sets And Special Integral Transforms Via Local Fractional Operators, Yang Xiaojun
Xiao-Jun Yang
The mappings for some special functions on Cantor sets are investigated. Meanwhile, we apply the local fractional Fourier series, Fourier transforms, and Laplace transforms to solve three local fractional differential equations, and the corresponding nondifferentiable solutions were presented.
Fourier Stability Analysis Of Two Finite Element Schemes For Reaction-Diffusion System With Fast Reversible Reaction, Ann J. Al-Sawoor Ph.D., Mohammed O. Al-Amr M.Sc.
Fourier Stability Analysis Of Two Finite Element Schemes For Reaction-Diffusion System With Fast Reversible Reaction, Ann J. Al-Sawoor Ph.D., Mohammed O. Al-Amr M.Sc.
Mohammed O. Al-Amr
In this paper, the stability analysis is performed on two Galerkin finite element schemes for solving reaction-diffusion system with fast reversible reaction. Fourier (Von Neumann) method is implemented to propose time-step criteria for the consistent and the lumped schemes with four popular choices for...
Discrete Adomian Decomposition Method For Solving Burger’S-Huxley Equation, Abdulghafor M. Al-Rozbayani Ph.D., Mohammed O. Al-Amr M.Sc.
Discrete Adomian Decomposition Method For Solving Burger’S-Huxley Equation, Abdulghafor M. Al-Rozbayani Ph.D., Mohammed O. Al-Amr M.Sc.
Mohammed O. Al-Amr
In this paper, the discrete Adomian decomposition method (DADM) is applied to a fully implicit scheme of the generalized Burger’s–Huxley equation. The numerical results of two test problems are compared with the exact solutions. The comparisons reveal that the proposed method is very accurate and effective for this kind of problems.
Approximation Solutions For Local Fractional Schrödinger Equation In The One-Dimensional Cantorian System, Xiao-Jun Yang
Approximation Solutions For Local Fractional Schrödinger Equation In The One-Dimensional Cantorian System, Xiao-Jun Yang
Xiao-Jun Yang
The local fractional Schr¨odinger equations in the one-dimensional Cantorian systemare investigated.The approximations solutions are obtained by using the local fractional series expansion method. The obtained solutions show that the present method is an efficient and simple tool for solving the linear partial differentiable equations within the local fractional derivative.
A Numerical Method For Solving Systems Of Fredholm Integral Equations By Collocation Linear Legendre Multi-Wavelets, Sa Edalatpanah, E Abdolmaleki
A Numerical Method For Solving Systems Of Fredholm Integral Equations By Collocation Linear Legendre Multi-Wavelets, Sa Edalatpanah, E Abdolmaleki
SA Edalatpanah
In this paper continuous Legendre multi-wavelets on the interval [0, 1) are utilized as a basis in collocation method to approximate the solutions of the Fredholm integral equations system. To begin with we describe the characteristic of Legendre multi-wavelets and will go on to indicate that through this method a system of Fredholm integral equations can be reduced to an algebraic equation. Finally, numerical results are given which support the theoretical results.
Convergence Analysis For Double Splitting Of Matrices, Hs Najafi, Sa Edalatpanah
Convergence Analysis For Double Splitting Of Matrices, Hs Najafi, Sa Edalatpanah
SA Edalatpanah
For single splittings of matrices, there are well-known convergence and comparison theorems. However, there are a few convergence theorems for double splitting. In this paper, we study this class of iterative methods. Furthermore, this paper gives new convergence results for double splitting of matrices.
A New Neumann Series Method For Solving A Family Of Local Fractional Fredholm And Volterra Integral Equations, Xiao-Jun Yang
A New Neumann Series Method For Solving A Family Of Local Fractional Fredholm And Volterra Integral Equations, Xiao-Jun Yang
Xiao-Jun Yang
We propose a new Neumann series method to solve a family of local fractional Fredholm and Volterra integral equations. The integral operator, which is used in our investigation, is of the local fractional integral operator type. Two illustrative examples show the accuracy and the reliability of the obtained results.
Analysis Of Fractal Wave Equations By Local Fractional Fourier Series Method, Xiao-Jun Yang
Analysis Of Fractal Wave Equations By Local Fractional Fourier Series Method, Xiao-Jun Yang
Xiao-Jun Yang
The fractal wave equations with local fractional derivatives are investigated in this paper.The analytical solutions are obtained by using local fractional Fourier series method. The present method is very efficient and accurate to process a class of local fractional differential equations.
Local Fractional Series Expansion Method For Solving Wave And Diffusion Equations On Cantor Sets, Yang Xiaojun
Local Fractional Series Expansion Method For Solving Wave And Diffusion Equations On Cantor Sets, Yang Xiaojun
Xiao-Jun Yang
We proposed a local fractional series expansion method to solve the wave and diffusion equations on Cantor sets. Some examples are given to illustrate the efficiency and accuracy of the proposed method to obtain analytical solutions to differential equations within the local fractional derivatives.
Approximate Solutions For Diffusion Equations On Cantor Space-Time, Xiao-Jun Yang
Approximate Solutions For Diffusion Equations On Cantor Space-Time, Xiao-Jun Yang
Xiao-Jun Yang
In this paper we investigate diffusion equations on Cantor space-time and we obtain approximate solutions by using the local fractional Adomian decomposition method derived from the local fractional operators. Analytical solutions are given in terms of the Mittag-Leffler functions defined on Cantor sets.
1-D Heat Conduction In A Fractal Medium: A Solution By The Local Fractional Fourier Series Method, Xiao-Jun Yang
1-D Heat Conduction In A Fractal Medium: A Solution By The Local Fractional Fourier Series Method, Xiao-Jun Yang
Xiao-Jun Yang
In this communication 1-D heat conduction in a fractal medium is solved by the local fractional Fourier series method. The solution developed allows relating the basic properties of the fractal medium to the local heat transfer mechanism.
Damped Wave Equation And Dissipative Wave Equation In Fractal Strings Within The Local Fractional Variational Iteration Method, Xiao-Jun Yang
Damped Wave Equation And Dissipative Wave Equation In Fractal Strings Within The Local Fractional Variational Iteration Method, Xiao-Jun Yang
Xiao-Jun Yang
No abstract provided.
A Numerical Approach On Hiemenz Ow Problem Using Radial Basis Functions, Saeid Abbasbandy, K. Parand, S. Kazem, A. R. Sanaei Kia
A Numerical Approach On Hiemenz Ow Problem Using Radial Basis Functions, Saeid Abbasbandy, K. Parand, S. Kazem, A. R. Sanaei Kia
Saeid Abbasbandy
In this paper, we propose radial basis functions (RBF) to solve the two dimensional flow of fluid near a stagnation point named Hiemenz flow. The Navier-Stokes equations governing the flow can be reduced to an ordinary diferential equation of third order using similarity transformation. Because of its wide applications the ow near a stagnation point has attracted many investigations during the past several decades. We satisfy boundary conditions such as infinity condition, by using Gaussian radial basis function through the both diferential and integral operations. By choosing center points of RBF with shift on one point in uniform grid, we …
A Cauchy Problem For Some Local Fractional Abstract Differential Equation With Fractal Conditions, Yang Xiaojun, Zhong Weiping, Gao Feng
A Cauchy Problem For Some Local Fractional Abstract Differential Equation With Fractal Conditions, Yang Xiaojun, Zhong Weiping, Gao Feng
Xiao-Jun Yang
Fractional calculus is an important method for mathematics and engineering [1-24]. In this paper, we review the existence and uniqueness of solutions to the Cauchy problem for the local fractional differential equation with fractal conditions \[ D^\alpha x\left( t \right)=f\left( {t,x\left( t \right)} \right),t\in \left[ {0,T} \right], x\left( {t_0 } \right)=x_0 , \] where $0<\alpha \le 1$ in a generalized Banach space. We use some new tools from Local Fractional Functional Analysis [25, 26] to obtain the results.
Mechaniczny Rozdział Faz Proj., Wojciech M. Budzianowski
Mechaniczny Rozdział Faz Proj., Wojciech M. Budzianowski
Wojciech Budzianowski
No abstract provided.
Challenges And Prospects Of Processes Utilising Carbonic Anhydrase For Co2 Separation, Patrycja Szeligiewicz, Wojciech M. Budzianowski
Challenges And Prospects Of Processes Utilising Carbonic Anhydrase For Co2 Separation, Patrycja Szeligiewicz, Wojciech M. Budzianowski
Wojciech Budzianowski
This article provides an analysis of processes for separation CO2 by using carbonic anhydrase enzyme with particular emphasis on reactive-membrane solutions. Three available processes are characterised. Main challenges and prospects are given. It is found that in view of numerous challenges practical applications of these processes will be difficult in near future. Further research is therefore needed for improving existing processes through finding methods for eliminating their main drawbacks such as short lifetime of carbonic anhydrase or low resistance of reactive membrane systems to impurities contained in flue gases from power plants.