Fractional Euler Limits and Their Applications

TL;DR

This paper explores fractional generalizations of Euler's formula, linking fractional calculus to applications like fractional compound interest, master equations, and Schlogl reactions with Mittag-Leffler waiting times.

Contribution

It introduces fractional Euler limits and demonstrates their relevance to various applications in fractional calculus and related fields.

Findings

Fractional Euler limits generalize classical Euler formulas.

Connections established between fractional calculus and master equations.

Application to Schlogl reactions with Mittag-Leffler waiting times.

Abstract

Generalisations of the classical Euler formula to the setting of fractional calculus are discussed. Compound interest and fractional compound interest serve as motivation. Connections to fractional master equations are highlighted. An application to the Schlogl reactions with Mittag-Leffler waiting times is described.