Francesco Mainardi
Core Contributions
Mainardi is a central figure in the field of fractional diffusion-wave equations. He systematically studied the application of the Mittag-Leffler function in fractional-order equations, established the fundamental solution theory for fractional diffusion and wave equations, and developed the probabilistic connection between random walks and fractional equations.
Selected Works
| Year | Work / Article | Problem Addressed |
|---|---|---|
| 1996 | "The fundamental solutions for the fractional diffusion-wave equation" | Derived the fundamental solutions for the time-fractional diffusion-wave equation, characterizing the continuous transition from diffusion to wave propagation using the Mittag-Leffler function |
| 2001 | "Fundamental solutions and asymptotic expansions for the fractional diffusion-wave equation" | Collaborated with Luchko and Pagnini to systematically establish the fundamental solution representation and asymptotic expansion theory for space-time fractional equations |
| 2010 | Fractional Calculus and Waves in Linear Viscoelasticity | Monograph that systematically connects fractional calculus with linear viscoelasticity theory, unifying the description of memory kernels and relaxation functions |