In this paper, a new fractional physics-informed neural networks (fPINNs) is proposed, which combines fPINNs with spectral collocation method to solve the time-fractional phase field models. Compared fPINNs, it has large representation capacity due property of method, reduces number approximate points discrete operators, improves training efficiency and higher error accuracy. Unlike traditional...

The variational iteration method(VIM) was extended to find approximate solutions of fractional chemical engineering equations. The Lagrange multipliers of the VIM were not identified explicitly. In this paper we improve the VIM by using concept of fixed point iteration method. Then this method was implemented for solving system of the time fractional chemical engineering equations. The ob...

In order to improve the time-frequency resolutions of short-time fractional Fourier transform, adaptive short-time fractional Fourier transform (ASTFRFT) method is used in this paper. The optimal order of ASTFRFT is given by maximizing kurtosis of signals in fractional domain, where the window width of ASTFRFT is searched by the maximal Shannon entropy of timefrequency distribution. Short-time ...

Distributed-order time-fractional wave equations appear in the modeling of propagation viscoelastic media. The material characteristics medium are modeled through constitutive functions or distributions distributed-order law. In this work we propose to take positive Radon measures for "functions". First, derive a thermodynamical restriction on which is easy check, and therefore suitable applica...