Newton’s Law of Cooling: A Fractional Approach

Year 2019, Volume: 19 Issue: 1, 60 - 66, 28.05.2019

Hüseyin Şirin Abdullah Engin Çalık

https://doi.org/10.35414/akufemubid.378360

Cited By: 2

Abstract

In this work, the
differential equation describing Newton's law of cooling has been redefined and
solved using Caputo fractional derivative. 
Unlike similar fractional solutions in the literature, this new solution
does not contain any time parameter.  
The obtained results have been compared with the experimental and the
standard ones. Order of fractional derivative which is most suitable for the
experimental results has been obtained.

Keywords

Newton’s Law of Cooling, Fractional Calculus, Fractional Derivative Order

Newton’un Soğuma Kanunu: Kesirsel Bir Yaklaşım

Abstract

Bu çalışmada Newton’un
soğuma kanununu tasvir eden diferansiyel denklem Caputo kesirsel türevi
kullanılarak yeniden tanımlanmış ve çözülmüştür. Bu yeni çözüm literatürdeki
benzer kesirsel çözümlerden farklı olarak herhangi bir zaman parametresi
içermemektedir. Elde edilen sonuçlar deneysel ve standart sonuçlarla
karşılaştırılmıştır. Deneysel sonuçlara en uygun olan kesirsel türev mertebesi
elde edilmiştir.

Keywords

Newton’un Soğuma Kanunu, Kesirsel Matematik, Kesirsel Türev Mertebesi

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