Closed-form solutions to fractional-order linear differential equations

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.