Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems

TL;DR

This paper introduces a new class of fractional derivatives of constant and variable orders, modeling anomalous relaxation in heat transfer, and compares their effectiveness in describing complex heat transfer phenomena.

Contribution

It is the first to address fractional derivatives of both constant and variable orders for relaxation equations in heat transfer.

Findings

Fractional derivatives effectively model complex heat transfer phenomena.

Comparative analysis shows differences among various fractional derivatives.

New fractional derivative models improve understanding of anomalous relaxation.

Abstract

In the present paper, we address a class of the fractional derivatives of constant and variable orders for the first time. Fractional-order relaxation equations of constants and variable orders in the sense of Caputo type are modeled from mathematical view of point. The comparative results of the anomalous relaxation among the various fractional derivatives are also given. They are very efficient in description of the complex phenomenon arising in heat transfer.