Closed-form solutions to fractional-order linear differential equations

Abstract

The definitions and properties of widely used fractional-order derivatives are summarized in this paper. The characteristic polynomials of the fractional-order systems are pseudo-polynomials whose powers of the complex variable are non-integers. This kind of systems can be approximated by high-order integer-order systems, and can be analyzed and designed by the sophisticated integer-order systems methodology. A new closed-form algorithm for fractional-order linear differential equations is proposed based on the definitions of fractional-order derivatives, and the effectiveness of the algorithm is illustrated through examples.

Keywords

fractional-order differentiator / linear systems / numerical solutions / calculus / simulation / differential equations / integer-order approximations