The flow heat conduction model and application based on time-space fractional derivative

Ai-Min Yang, Yu-Zhu Zhang, Yue

Abstract

This paper first introduces fractional operators to heat conduction equation model, and processes the derivative of space and time item using the fractional order, establishes a time - space fractional derivative flow model, and grids the difference of the model, give the implicate difference scheme for the model, and proves the convergence and stability of the algorithm; After that ,combining with examples, calculates the numerical solution of the model, draws the graph of temperature field, and analyzes the fractional order derivative's influence on the temperature field in space and time. The results indicate that the temperature field on the fractional derivative order has strong sensitivity