A new fractional operator of variable order: application in the description of anomalous diffusion

TL;DR

This paper introduces a novel variable-order fractional operator based on Caputo derivatives, analyzing its properties and demonstrating its effectiveness in modeling complex anomalous diffusion processes.

Contribution

It proposes a new fractional operator of variable order using a monotonic increasing function, expanding the tools for modeling anomalous diffusion.

Findings

The operator's properties are characterized in Laplace and Fourier domains.

The operator effectively models anomalous diffusion with complex transport behaviors.

The formulation improves the description of concentration dynamics in complex systems.

Abstract

In this paper, a new fractional operator of variable order with the use of the monotonic increasing function is proposed in sense of Caputo type. The properties in term of the Laplace and Fourier transforms are analyzed and the results for the anomalous diffusion equations of variable order are discussed. The new formulation is efficient in modeling a class of concentrations in the complex transport process.