"A Fractional Calculus Approach to Study Newton’s Law of Cooling" by Nikita Bhangale and Krunal B. Kachhia

Progress in Fractional Differentiation & Applications

Article Title

A Fractional Calculus Approach to Study Newton’s Law of Cooling

Authors

Nikita Bhangale, Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology (CHARUSAT), Changa, Anand-388421, Gujarat, IndiaFollow
Krunal B. Kachhia, Department of Mathematical Sciences, P. D. Patel Institute of Applied Sciences, Charotar University of Science and Technology (CHARUSAT), Changa, Anand-388421, Gujarat, IndiaFollow

Author Country (or Countries)

India

Abstract

This paper deals with the application of a novel variable-order and constant-order fractional derivatives in the Newton’s law of cooling. The variable-order fractional derivative can be set as a smooth function, bounded on (0,1], while the constant-order fractional derivative can be set as a fractional equation, bounded on (0,1]. We solved analytically the fractional equations using the Laplace transform. Numerical simulations were performed for different values of fractional order. The integer-order classical model is recovered when the order of the fractional derivative is equal to 1. Based upon the results obtained, the efficiency rates of the fractional-order operators with non-singular kernel are higher than that of the existing fractional model with singular kernel.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/pfda/080207

Recommended Citation

Bhangale, Nikita and B. Kachhia, Krunal (2022) "A Fractional Calculus Approach to Study Newton’s Law of Cooling," Progress in Fractional Differentiation & Applications: Vol. 8: Iss. 2, Article 7.
DOI: http://dx.doi.org/10.18576/pfda/080207
Available at: https://digitalcommons.aaru.edu.jo/pfda/vol8/iss2/7

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