Michele Caputo
Core Contributions
Caputo proposed the Caputo fractional derivative, which naturally embeds integer-order initial value conditions into fractional differential equations. The Caputo derivative adopts a "differentiate first, then integrate" approach, allowing physical initial conditions (displacement, velocity) to be used directly, greatly advancing the application of fractional calculus in physics and engineering.
Selected Works
| Year | Work / Article | Problem Addressed |
|---|---|---|
| 1967 | "Linear models of dissipation whose Q is almost frequency independent" | Proposed the definition of the Caputo fractional derivative, resolving the issue of ambiguous physical meaning of initial value conditions in the Riemann-Liouville derivative |
| 1971 | Elasticità e Dissipazione (Elasticity and Dissipation) | Applied the Caputo derivative to the modeling of viscoelastic materials, demonstrating that fractional-order models can better describe the memory effects of real materials |
| 2001 | "Distributed order differential equations modelling dielectric induction and diffusion" | Collaborated with Fabrizio to extend the Caputo derivative to the distributed-order case, used to describe diffusion processes in non-homogeneous media |