<p>In this article, Newton’s classical law of cooling is revisited using a generalized Caputo-type derivative. One of the fundamental assumptions of the classical model is that the system’s behavior depends solely on the instantaneous temperature difference. However, in many physical processes, memory effects and past-dependent influences play a significant role. Therefore, in this work, the concept of fractional derivatives is applied in its generalized form to capture these dynamic behaviors that the classical model fails to explain. The solution of the model is obtained analytically using the Laplace integral transform method, and the results are compared with both the classical solution and the Caputo fractional derivative solution commonly found in the literature. Analyses conducted through numerical examples indicate that the generalized model provides a wider range of dynamic responses compared to the classical model and may better represent temperature variations, capturing the system’s memory effects more effectively. The findings demonstrate that the generalized Caputo-type derivative can more effectively model the system’s memory effects, thus yielding more accurate results than the classical approach. In conclusion, the proposed method not only offers a novel perspective on Newton’s law of cooling but also provides a robust alternative for modeling similar physical systems.</p>

错误:搜索内容不能为空,请输入英文关键词
错误:关键词超出字数限制,请精简
高级检索

A novel fractional calculus approach to Newton’s law of cooling: numerical examples and comparative analysis of dynamic behaviors

  • Enes Ata

摘要

In this article, Newton’s classical law of cooling is revisited using a generalized Caputo-type derivative. One of the fundamental assumptions of the classical model is that the system’s behavior depends solely on the instantaneous temperature difference. However, in many physical processes, memory effects and past-dependent influences play a significant role. Therefore, in this work, the concept of fractional derivatives is applied in its generalized form to capture these dynamic behaviors that the classical model fails to explain. The solution of the model is obtained analytically using the Laplace integral transform method, and the results are compared with both the classical solution and the Caputo fractional derivative solution commonly found in the literature. Analyses conducted through numerical examples indicate that the generalized model provides a wider range of dynamic responses compared to the classical model and may better represent temperature variations, capturing the system’s memory effects more effectively. The findings demonstrate that the generalized Caputo-type derivative can more effectively model the system’s memory effects, thus yielding more accurate results than the classical approach. In conclusion, the proposed method not only offers a novel perspective on Newton’s law of cooling but also provides a robust alternative for modeling similar physical systems.