Anatoly Kochubei
Core Contributions
Kochubei is an important contributor to the theory of distributed-order calculus and fractional diffusion equations. He systematically studied the fundamental solutions and asymptotic behavior of distributed-order differential equations, and connected fractional calculus with p-adic analysis, pioneering fractional analysis on non-Archimedean fields.
Selected Works
| Year | Work / Article | Problem Addressed |
|---|---|---|
| 2004 | "Cauchy problem for fractional diffusion equations" (with Eidelman) | Established the well-posedness theory for the Cauchy problem of space-time fractional diffusion equations, proving the existence and regularity of fundamental solutions |
| 2008 | "Distributed order calculus and equations of ultraslow diffusion" | Systematically established the mathematical theory of distributed-order calculus, solving the modeling problem of ultraslow diffusion processes and proving the logarithmic decay behavior of solutions |
| 2001 | "Pseudo-differential equations and stochastics over non-Archimedean fields" | Combined fractional operators with p-adic analysis, pioneering the theory of pseudo-differential equations and stochastic processes on non-Archimedean fields |