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Articles 1 - 7 of 7
Full-Text Articles in Non-linear Dynamics
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.
On The Semi-Inverse Method And Variational Principle, Xue-Wei, Li, Ya Li, Ji-Huan He
On The Semi-Inverse Method And Variational Principle, Xue-Wei, Li, Ya Li, Ji-Huan He
Ji-Huan He
In this Open Forum, Liu et al. proved the equivalence between He-Lee 2009 variational principle and that by Tao and Chen (Tao, Z. L., Chen, G. H., Thermal Science, 17(2013), pp. 951-952) for one dimensional heat conduction. We confirm the correction of Liu et al.’s proof, and give a short remark on the history of the semi-inverse method for establishment of a generalized variational principle.
Exp-Function Method For Fractional Differential Equations, Ji-Huan He
Exp-Function Method For Fractional Differential Equations, Ji-Huan He
Ji-Huan He
A fractional nonlinear wave equation is used as an example to elucidate how to solve fractional differential equations with local fractional derivatives via the fractional complex transform and the exp-function method.
Fractal Approach To Heat Transfer In Silkworm Cocoon Hierarchy, Dong-Dong Fei, Fu-Juan Liu, Qiu-Na Cui, Ji-Huan He
Fractal Approach To Heat Transfer In Silkworm Cocoon Hierarchy, Dong-Dong Fei, Fu-Juan Liu, Qiu-Na Cui, Ji-Huan He
Ji-Huan He
Silkworm cocoon has a complex hierarchic structure with discontinuity. In this paper, heat transfer through the silkworm cocoon is studied using fractal theory. The fractal approach has been successfully applied to explain the fascinating phenomenon of cocoon survival under extreme temperature environment. A better understanding of heat transfer mechanisms for the cocoon could be beneficial to the design of biomimetic clothes for special applications.
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.