Generalized variational principle and periodic wave solution to the modified equal width-Burgers equation in nonlinear dispersion media

Under investigation in this paper are two local fractional partial differential systems, one is the homogeneous linear partial differential system with initial values, and the other is the inhomogeneous non-linear partial differential system with initial and boundary values. To solve these two local fractional systems, we employ the local fractional variational iteration method and obtain exact solutions. It is shown that the method provides an effective mathematical tool for solving linear and non-linear local fractional partial differential systems with initial and boundary values.

Section: Discussionmentioning

confidence: 99%

Variational iteration method for two fractional systems with boundary conditions

Zhang

2022

“…( 18)-( 20). The variational principle is also a useful tool for both analytical and numerical solutions [19][20][21][22][23][24].…”

Section: Conservation Laws and Variational Principlementioning

confidence: 99%

Thermodynamical properties of rotating disk electrodes for second order ECE reactions

Liu

2022

The thermodynamical model for rotating disk electrodes for second order ECE (electrochemical-chemical-electrochemical) reactions is considered, and the effect of concentrations of three species on the current for ECE reaction is theoretically analyzed, and the optimal current value is obtained. The Taylor series method is used, the derivation is simple and the accuracy can be improved if higher order Taylor series is considered. A fractal modification is also suggested for future research.

“…It is generally difficult to solve non-linear fractional partial differential equations. In the last two decades, some analytical methods for solving non-linear differential equations can be extended to solve fractional differential equations, for example, the variational method [8][9][10][11][12][13], the variational iteration method [14][15][16][17][18], the homotopy perturbation method [19,20], the direct algebraic method [21,22], the exp-function method [23], the Fourier spectral method [24], the reproducing kernel method [25]. The FPSM was proposed by El-Ajou et al [1], and recently, many researchers [26][27][28][29][30][31] have obtained the series solution of fractional differential equations by using FPSM.…”

Section: Introductionmentioning

confidence: 99%

Approximate analytical solution of time-fractional non-linear heat equation via fractional power series method

Deng

2022