Newton’s law of cooling with generalized conformable derivatives

Miguel Vivas-Cortez; Alberto Fleitas; Paulo M. Guzmán; Juan E. Nápoles; Juan J. Rosales

doi:10.3390/sym13061093

Newton’s law of cooling with generalized conformable derivatives

Miguel Vivas-Cortez^*, Alberto Fleitas, Paulo M. Guzmán, Juan E. Nápoles, Juan J. Rosales

^*Corresponding author for this work

Faculty of Exact and Natural Sciences

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

In this communication, using a generalized conformable differential operator, a simulation of the well-known Newton’s law of cooling is made. In particular, we use the conformable t^1−α, e^(1−α)t and non-conformable t^−α kernels. The analytical solution for each kernel is given in terms of the conformable order derivative 0 < α ≤ 1. Then, the method for inverse problem solving, using Bayesian estimation with real temperature data to calculate the parameters of interest, is applied. It is shown that these conformable approaches have an advantage with respect to ordinary derivatives.

Original language	English
Article number	1093
Journal	Symmetry
Volume	13
Issue number	6
DOIs	https://doi.org/10.3390/sym13061093
State	Published - 21 Jun 2021

Bibliographical note

Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Funding

Funding: This research was funded by the Department of Electrical Engineering and by the Division of Engineering, Campus Irapuato-Salamanca, both from the University of Guanajuato (México).

Funders	Funder number
Department of Electrical Engineering
Division of Engineering
Universidad de Guanajuato

Keywords

Conformable derivative
Fractional calculus
Newton law of cooling

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title = "Newton{\textquoteright}s law of cooling with generalized conformable derivatives",

abstract = "In this communication, using a generalized conformable differential operator, a simulation of the well-known Newton{\textquoteright}s law of cooling is made. In particular, we use the conformable t1−α, e(1−α)t and non-conformable t−α kernels. The analytical solution for each kernel is given in terms of the conformable order derivative 0 < α ≤ 1. Then, the method for inverse problem solving, using Bayesian estimation with real temperature data to calculate the parameters of interest, is applied. It is shown that these conformable approaches have an advantage with respect to ordinary derivatives.",

keywords = "Conformable derivative, Fractional calculus, Newton law of cooling",

author = "Miguel Vivas-Cortez and Alberto Fleitas and Guzm{\'a}n, {Paulo M.} and N{\'a}poles, {Juan E.} and Rosales, {Juan J.}",

note = "Publisher Copyright: {\textcopyright} 2021 by the authors. Licensee MDPI, Basel, Switzerland.",

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AU - Vivas-Cortez, Miguel

AU - Fleitas, Alberto

AU - Guzmán, Paulo M.

AU - Nápoles, Juan E.

AU - Rosales, Juan J.

PY - 2021/6/21

Y1 - 2021/6/21

N2 - In this communication, using a generalized conformable differential operator, a simulation of the well-known Newton’s law of cooling is made. In particular, we use the conformable t1−α, e(1−α)t and non-conformable t−α kernels. The analytical solution for each kernel is given in terms of the conformable order derivative 0 < α ≤ 1. Then, the method for inverse problem solving, using Bayesian estimation with real temperature data to calculate the parameters of interest, is applied. It is shown that these conformable approaches have an advantage with respect to ordinary derivatives.

AB - In this communication, using a generalized conformable differential operator, a simulation of the well-known Newton’s law of cooling is made. In particular, we use the conformable t1−α, e(1−α)t and non-conformable t−α kernels. The analytical solution for each kernel is given in terms of the conformable order derivative 0 < α ≤ 1. Then, the method for inverse problem solving, using Bayesian estimation with real temperature data to calculate the parameters of interest, is applied. It is shown that these conformable approaches have an advantage with respect to ordinary derivatives.

KW - Conformable derivative

KW - Fractional calculus

KW - Newton law of cooling

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VL - 13

JO - Symmetry

JF - Symmetry

IS - 6

M1 - 1093

ER -

Newton’s law of cooling with generalized conformable derivatives

Abstract

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Keywords

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