Solving FDE by trigonometric neural network and its applications in simulating fractional HIV model and fractional Schrodinger equation

Abstract

In this paper, we put forward numerical algorithms to simulate fractional HIV infected CD4+T cell model and fractional Schrodinger equation. First, we put forward numerical algorithm to solve fractional differential systems with trigonometric neural network. Then trigonometric neural network method is used to simulate the fractional HIV infected CD4+T cell model. It is found that the infection equilibrium has the restriction condition for the number of virus particles released by each infected cell. Under this condition, the fractional system has a unique positive equilibrium. Second, we put forward numerical algorithm to solve fractional PDE with trigonometric neural network. Then this numerical method is used to simulate fractional Schrodinger equation, and some important results in fractional quantum mechanics are concluded by the corresponding numerical results.