Fractional differential and integral operations and cumulative processes

TL;DR

This paper develops a general formula for fractional calculus operations using fractal operators, revealing their effectiveness in modeling complex systems and connecting them to physical phenomena.

Contribution

It introduces a new general formula for fractional differential and integral operations via fractal operators, enhancing understanding of their role in complex system modeling.

Findings

Derived a general formula for fractional calculus operations.

Linked fractional calculus to physical complex systems.

Uncovered mechanisms behind fractional calculus success in complex modeling.

Abstract

In this study the general formula for differential and integral operations of fractional calculus via fractal operators by the method of cumulative diminution and cumulative growth is obtained. The under lying mechanism in the success of traditional fractional calculus for describing complex systems is uncovered. The connection between complex physics with fractional differentiation and integration operations is established.