Caputo

Caputo is an Italian surname. The name is found throughout Italy and among Italian-descended communities, and it is borne by many individuals across various professions, including science, culture, and public life. In addition to its use as a family name, Caputo appears in academic contexts related to mathematics and applied sciences.

In mathematics and applied sciences, Caputo refers to the Caputo fractional derivative, a standard formulation of a fractional derivative used in modeling anomalous diffusion and viscoelastic phenomena. The Caputo derivative is named after Italian mathematician Michele Caputo. For a function f defined on [0, ∞) and with n−1 < α < n, the Caputo derivative of order α is given by D^α f(t) = (1/Γ(n−α)) ∫_0^t f^(n)(ξ) (t−ξ)^{n−α−1} dξ, where f^(n) is the n-th derivative of f. This form is often preferred in physical problems because its initial conditions resemble those of classical differential equations.

The Caputo surname has appeared in various other contexts as well, including notable individuals in science, the arts, and public life. The name remains one of many Italian surnames that have contributed to global academia and culture.