Fractional-order Variational Derivative

TL;DR

This paper explores approaches to defining fractional-order variational derivatives, proposing a fractional generalization of Gateaux differential to establish a consistent framework for fractional variations.

Contribution

It introduces a fractional generalization of Gateaux differential to define fractional-order variational derivatives.

Findings

Proposes a fractional generalization of Gateaux differential.

Discusses problems in formulating fractional variational derivatives.

Lays groundwork for consistent fractional calculus in variational analysis.

Abstract

We consider some possible approaches to the fractional-order generalization of definition of variation (functional) derivative. Some problems of formulation of a fractional-order variational derivative are discussed. To give a consistent definition of the fractional-order variations, we use a fractional generalization of Gateaux differential.