Transformation Property of the Caputo Fractional Differential Operator in Two Dimensional Space

TL;DR

This paper derives how the Caputo fractional derivative operator transforms under rotation in two-dimensional space, which is crucial for applying fractional calculus in multi-dimensional physics and dynamics.

Contribution

It provides the first detailed derivation of the transformation property of the Caputo fractional derivative under rotation in 2D space.

Findings

The transformation property under rotation is explicitly derived.

An illustrative example demonstrates the application of the derived property.

The results facilitate the integration of fractional calculus into multi-dimensional physical models.

Abstract

The transformation property of the Caputo fractional derivative operator of a scalar function under rotation in two dimensional space is derived. The study of the transformation property is essential for the formulation of fractional calculus in multi-dimensional space. The inclusion of fractional calculus in the Lagrangian and Hamiltonian dynamics relies on such transformation. An illustrative example is given.