The Yang Laplace transform- DJ iteration method for solving the local fractional differential equation

Abstract

In this paper, we propose the Yang Laplace transform-DJ iteration method, which is derived from coupling the YangLaplace transform method with the DJ iteration method. The solution procedure for the local fractional differential equations is given. And some test examples are given to show the accuracy and the validity of the proposed technique.

Fractional residual method coupled with Adomian decomposition method for solving local fractional differential equations

“…Fractal theory is also a powerful tool to the analysis of biologic and material phenomena [11,12]. How to solve such problems has become a hot topic in mathematics, and some effective methods have appeared in literature, e.g., the variational iteration method [13][14][15], the fractional residual method [16], the homotopy perturbation method [17][18][19][20], the local fractional Fourier series method [21][22][23], The Yang Laplace transform-DJ iteration method [24], He-Laplace method [25,26], the fractional complex transform (two-scale transform) [27,28], the coupled method of the variational iteration and reduced differential transform method [29], the differential transform approach [30], the asymptotic perturbation method [31], the coupled method of the Sumudu transform and the variational iteration method [32], the direct algebraic method [33,34], the exp-function method [35], the variational approach [36][37][38][39], the Fourier spectral method [40] and the reproducing kernel method [41].…”

An improved homotopy perturbation method for solving local fractional nonlinear oscillators

“…There are many computational methods for handling these fractional differential equations, such as the reduced differential transform method, 22 the transform methods, 23 the Yang Laplace transform-DJ iteration method, 24 the local fractional Fourier method, 25,26 and others. [15][16][17] Fractional oscillation equations arise in various areas of engineering and applied sciences, which are used as a powerful tool to vibration isolation and reduction of unnecessary vibration by porous media.…”