Mathematical aspects of application of fractional multidimensional Fokker-Plank equation to the theory of rate of chemical reactions based on spectroscopy experiments with examples.

Abstract

Different types of spectroscopy experiments carried by multiple teams suggest some discrepancies between one-dimensional (1D) Kramers’ theory for the rate of chemical reactions with hydrodynamic Stokes-Einstein friction model. The disagreement continued despite multidimensional (multi-D), or non-Markovian, or not-exactly hydrodynamic modifications by Grote-Hynes, Hubbard, and other authors. The proposed fractional dimensional modification to multi-D model is based on theoretical and experimental findings of dimensional disagreement and deceptive simplicity between curves for barrier crossing at equilibrium and the boundary of the curves. Comparison of less anomalous fractional derivative exponents of 1.9 and 1.7 with more anomalous of 1.5 and 1.3 suggest Sierpinski carpet, Cesaro’s, and different attractors’ curves.