An evolutionary interpretation of the \(p\)-adic ultrametric diffusion equation (Q2377494)

A basic point of the \(p\)-adic analysis proposed by \textit{V. S. Vladimirov}, \textit{I. V. Volovich} and \textit{E. I. Zelenov} [\(p\)-adic analysis and mathematical physics, Moskva: VO Nauka. 352 p. (1994; Zbl 0864.46048)] is the following \(p\)-adic analogue of the diffusion equation: \[ {\partial f/\partial t}+ D^\lambda_x f= 0, \] where \(D^\lambda_x\) is an analogue of the classical fractional derivative. The authors propose here this equation as an effective model for the biological evolution, emphsizing that \(p\)-adic analysis turns out to be more appropriate than classical analysis in the description of the biological referents.