Optimization of Fractional Order Dynamic Chemical Processing Systems

Abstract

In this work we address the dynamic simulation and optimization of chemical processing systems modeled in terms of fractional order differential equations. While fractional derivatives were first proposed by Liouville in 1832 [Samko et al. Fractional Integrals and Derivatives Theory and Applications; Gordon and Breach: New York, 1993; Oldham and Spanier. The fractional Calculus; Academic Press: New York, 1974], fractional differential equation (FDE) models have been only recently been explored. These have been proposed for a wide range of applications that include systems with nonlocal diffusion phenomena and geometries with fractal dimensions. FDE models have been shown to have advantages over traditional integer order models, as they often avoid scale dependent model parameters. For medium or large scale applications of FDEs normally no analytical solutions are available, and therefore, approximated numerical solutions ought to be sought. Moreover, little work has been done to solve fractional order dif...