Zeta-management: categorical and fractional differential approaches

Abstract

The aim of this note is to introduce and justify the reasons why the traditional differential approach of complex systems, and more specifically non-additive systems, must be recognized as an epistemological failure (e.g. in economy, finance or limited in social agent models). The categorical character of the context proper to any type of irreversible exchange is analyzed. This approach underlines and explains the weaknesses of the set theory generally utilized. Beyond the mathematical concepts their application in project management provides an illustrative example allowing an easy understanding of the statements of problems attached to non-additive and irreversible complex system. We will see why it is necessary to shift the analysis from the set theory toward the theory of categories and why this choice very naturally introduces the use of non- integer order Differential Equations.