A New Perspective on Newton's Law of Cooling in Frame of Newly Defined Fractional Conformable Derivative

TL;DR

This paper introduces a new fractional conformable derivative to reformulate Newton's law of cooling, demonstrating improved alignment with experimental data over traditional integer-order models through numerical and error analysis.

Contribution

It presents a novel fractional conformable derivative approach to Newton's law of cooling, enhancing model accuracy with real data compared to classical methods.

Findings

Fractional conformable derivative yields better data fit.

Optimal fractional orders identified for improved accuracy.

Numerical analysis supports advantages over integer derivatives.

Abstract

In this paper, Newton's law of cooling is considered from a different perspective with newly defined fractional conformable. Obtained results are compared with experimental results and found optimal fractional orders which fit better with real data. Results show that Newton's law of cooling with fractional conformable derivative gives better results to integer order derivative. Results are given comparatively to Newton's law of cooling with integer order and experimental data and also, fractional conformable derivative's advantages are supported by numerical illustrations and error analysis.