Parameter estimation for uncertain fractional differential equations

Since the concept of uncertain fractional differential equations was proposed, its wide range of applications have urged us to consider parameter estimation for uncertain fractional differential equations. In this paper, based on the definition of Liu process, we construct a function of unknown parameters which follows a standard normal uncertainty distribution. Then the method of moments is used to build a system of equations whose solutions are the estimated values of unknown parameters. After that, an algorithm of parameter estimation for a special uncertain fractional differential equation is proposed. Finally, the algorithm is applied to two numerical examples and the acceptability of the estimated parameters is proved by using uncertain hypothesis test.

Automated summary

This paper discusses the parameter estimation problem for uncertain fractional differential equations and proposes an algorithm based on the definition of Liu process and the method of moments. The effectiveness of the algorithm is demonstrated through numerical examples and uncertain hypothesis test.