Michele Caputo: a scientist from Geodesy, far beyond Geodesy

The scientific figure of Michele Caputo is illustrated showing how his conceptual trajectory, starting from the invention of important mathematical tools, has carried him into a number of different disciplines where such tools could be used; primarily Economics and Probability. After an introduction, in §2, 3, and 4, we illustrate the typical geodetic march through measurements, models and methods that Caputo has followed in his career. In §5 we concentrate on the invention of the famous Caputo’s operator, a fractional derivative, describing its rigorous definition and mathematical properties and illustrating general Cauchy problems based on it. In §6 we present two examples: one is classical, where the fractional derivative is employed to describe the mechanical energy dissipation of body waves crossing the Earth; the second example describes an application to renewal models, in particular to fractional Poisson process, demonstrating the loss of Markov property and the rise of a memory dependent model. Some conclusions close the paper.