Newton’s Law of Cooling with Generalized Conformable Derivatives

Symmetry

Juan J. Rosales¹  Miguel Vivas-Cortez²  Juan E. Nápoles³  Paulo M. Guzmán³  Alberto Fleitas⁴ 

[1] División 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, Mexico;Escuela 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, Ecuador;Facultad de Ciencias Exactas y Naturales y Agrimensura, Universidad Nacional del Nordeste, Corrientes 3400, Argentina;Facultad de Matemáticas, Universidad Autónoma de Guerrero, Acapulco 39070, Guerrero, Mexico;

关键词: fractional calculus;    conformable derivative;    Newton law of cooling;   

DOI  :  10.3390/sym13061093

来源: DOAJ

【 摘 要 】

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 $t^{1-\alpha }$, $e^{(1-\alpha )t}$ and non-conformable $t^{-\alpha }$ kernels. The analytical solution for each kernel is given in terms of the conformable order derivative $0<\alpha \le 1$. 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.

【 授权许可】

Unknown