Application of fractional calculus to the analysis of Laplace transformed data

This paper describes a novel method using fractional calculus to estimate non-integer moments of a random variable from the measured Laplace transform of its probability density function. We demonstrate that the ω-th moment (ω ϵ R) of the random variable can be directly obtained by a linear transformation of the data. When w > 0, computation of moments corresponds to fractional integration of the data. When ω ≤ 0, computation of moments corresponds to fractional differentiation.