Computational Method And Application Of Caputo-Fabrizio Fractional Derivative By Using Lagrange Interpolation

The random walk model is one of the most intuitive and effective models that use statistical physical methods to describe the diffusion process.It is derived from the numerical simulation of the Brownian motion of matter particles and is used to describe abnormal diffusion phenomena with different characteristics.The fractional diffusion equation model is a recent model.The important research method that has emerged to study abnormal diffusion.It has non-local features and is usually used to simulate abnormal diffusion processes with memory or long-range correlation.The Caputo-Fabrizio fractional derivative can better describe the complete memory because it does not contain singular kernel.Effects are often used in numerical simulations in modern science and technology,such as control systems,physics,medicine,fluid dynamics and other disciplines,and gradually applied to various fields of engineering science.In this paper,based on the idea of Lagrange polynomial interpolation,combined with the numerical integration method,for the Caputo-Fabrizio time fractional derivative,an efficient and easy-to-operate numerical computational algorithm with high precision is constructed,and the numerical algorithm is applied to the solute convective diffusion transport.In the fractional diffusion model,the algorithm of the Caputo-Fabrizio time fractional diffusion model is further derived and numerically simulated,and the results show the effectiveness of the method.This article introduces the research background of fractional derivatives.In the preliminary knowledge section,including Lagrange interpolation and error...