Newton’s Law of Cooling with Generalized Conformable Derivatives
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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><se...
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MDPI AG
2021-06-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/6/1093 |
| _version_ | 1797529441796096000 |
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| author | Miguel Vivas-Cortez Alberto Fleitas Paulo M. Guzmán Juan E. Nápoles Juan J. Rosales |
| author_facet | Miguel Vivas-Cortez Alberto Fleitas Paulo M. Guzmán Juan E. Nápoles Juan J. Rosales |
| author_sort | Miguel Vivas-Cortez |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>t</mi><mrow><mn>1</mn><mo>−</mo><mi>α</mi></mrow></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>e</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>α</mi><mo stretchy="false">)</mo><mi>t</mi></mrow></msup></semantics></math></inline-formula> and non-conformable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>t</mi><mrow><mo>−</mo><mi>α</mi></mrow></msup></semantics></math></inline-formula> kernels. The analytical solution for each kernel is given in terms of the conformable order derivative <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>α</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>. 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. |
| first_indexed | 2024-03-10T10:13:55Z |
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| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T10:13:55Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-a7ecd33ba32c4e67b4f572dac3f49eb52023-11-22T00:58:43ZengMDPI AGSymmetry2073-89942021-06-01136109310.3390/sym13061093Newton’s Law of Cooling with Generalized Conformable DerivativesMiguel Vivas-Cortez0Alberto Fleitas1Paulo M. Guzmán2Juan E. Nápoles3Juan J. Rosales4Escuela de Ciencias Físicas y Matemáticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Católica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, EcuadorFacultad de Matemáticas, Universidad Autónoma de Guerrero, Acapulco 39070, Guerrero, MexicoFacultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Corrientes 3400, ArgentinaFacultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Corrientes 3400, ArgentinaDivisión de Ingenierías Campus Irapuato-Salamanca, Universidad de Guanajuato, Carretera Salamanca-Valle de Santiago, km. 3.5+1.8, Comunidad de Palo Blanco, Salamanca 36760, Guanajuato, MexicoIn 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>t</mi><mrow><mn>1</mn><mo>−</mo><mi>α</mi></mrow></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>e</mi><mrow><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>α</mi><mo stretchy="false">)</mo><mi>t</mi></mrow></msup></semantics></math></inline-formula> and non-conformable <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>t</mi><mrow><mo>−</mo><mi>α</mi></mrow></msup></semantics></math></inline-formula> kernels. The analytical solution for each kernel is given in terms of the conformable order derivative <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>0</mn><mo><</mo><mi>α</mi><mo>≤</mo><mn>1</mn></mrow></semantics></math></inline-formula>. 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.https://www.mdpi.com/2073-8994/13/6/1093fractional calculusconformable derivativeNewton law of cooling |
| spellingShingle | Miguel Vivas-Cortez Alberto Fleitas Paulo M. Guzmán Juan E. Nápoles Juan J. Rosales Newton’s Law of Cooling with Generalized Conformable Derivatives Symmetry fractional calculus conformable derivative Newton law of cooling |
| title | Newton’s Law of Cooling with Generalized Conformable Derivatives |
| title_full | Newton’s Law of Cooling with Generalized Conformable Derivatives |
| title_fullStr | Newton’s Law of Cooling with Generalized Conformable Derivatives |
| title_full_unstemmed | Newton’s Law of Cooling with Generalized Conformable Derivatives |
| title_short | Newton’s Law of Cooling with Generalized Conformable Derivatives |
| title_sort | newton s law of cooling with generalized conformable derivatives |
| topic | fractional calculus conformable derivative Newton law of cooling |
| url | https://www.mdpi.com/2073-8994/13/6/1093 |
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