摘要：AbstractAn ancient topic as this paper focuses on, some innovative insightful interesting observations are surely provided. On one hand, by expanding the range of integration order in Riemann-Liouville derivative and Caputo derivative, a new type of definitions are given for fractional order derivatives. On the other hand, a novel representation based on Taylor series is formulated, which is helpful to unravel some uncanny feature and handle some hard issues. The advantage of the proposed results lies in that a deeper understanding of fractional order calculus is achieved and it facilitates the relevant application.
关键词：KeywordsFractional order calculusIntegration orderSingularityTaylor series
