Economic interpretation of fractional derivatives

TL;DR

This paper proposes an economic interpretation of fractional derivatives, specifically Caputo derivatives, as indicators that generalize average and marginal values to describe economic processes with memory.

Contribution

It introduces the T-indicator concept, linking fractional derivatives to economic indicators with memory, extending traditional average and marginal values.

Findings

Fractional derivatives are interpreted as intermediate economic indicators.

The T-indicator generalizes average and marginal values.

Fractional derivatives describe processes with memory.

Abstract

An economic interpretation of the Caputo derivatives of non-integer orders is proposed. The suggested economic interpretation of the fractional derivatives is based on a generalization of average and marginal values of economic indicators. We formulate an economic interpretation by using the concept of the T-indicator that allows us to describe economic processes with memory. The standard average and marginal values of indicator are special cases of the proposed T-indicator, when the order is equal to zero and one, respectively. The fractional derivatives are interpreted as economic characteristics (indicators) that are intermediate between the standard average and marginal values of indicators.