La derivada conformable y sus aplicaciones en ingeniería
DOI:
https://doi.org/10.29105/ingenierias23.88-3Palabras clave:
Ecuación diferencial, cálculo fraccional, modelado, derivada conformableResumen
En este trabajo se describen algunas aplicaciones de la derivada conformable en la solución de ecuaciones diferenciales de orden fraccionario. Las derivadas de orden no entero son presentadas en función del tiempo para resolver el modelo de Maxwell, el circuito eléctrico RC en serie y la ley de enfriamiento de Newton. Los resultados obtenidos muestran la variación del parámetro α del operador fraccional conformable para modelar el comportamiento de los fenómenos propuestos. Se obtiene que los parámetros esfuerzo, corriente eléctrica y temperatura en función del tiempo, presentan un decaimiento más pronunciado a medida que α disminuye. La derivada conformable es una herramienta matemática que permite resolver ecuaciones diferenciales de orden fraccionario en una forma más simple.
Descargas
Métricas
Citas
Hilfer, R. Applications of Fractional Calculus in Physics. Universität Mainz & Universität Stuttgart, Germany, 2000.
Baleanu, D. New Trends in Nanotechnology and Fractional Calculus Applications. Springer, 2010.
Das,S.KindergartenofFractionalCalculus.CambridgeScholarsPublishing, 2020.
Sánchez-Muñoz,J.M.Génesisydesarrollodelcálculofraccional.Pensamiento Matemático, 1, 2011, 15 pp.
Reyes-Melo, M.E., González-González, V.A., Guerrero-Salazar, C.A., García-Cavazos, F., Ortiz-Méndez, U. Application of fractional calculus to the modeling of the complex rheological behavior of polymers: From the glass transition to flow behavior. I. The theoretical model. Journal of Applied Polymer Science, 108, 2008, 731-737.
Buesaquillo-Gómez V.G., Pérez-Riascos A., Rugeles-Pérez A. Cálculo fraccional. Revista de Ciencias, 4 (1), 2014, 16 pp.
Capelas-deOliveira,E.,Tenreiro-Machado,J.A.Areviewofdefinitionsfor fractional derivatives and integral. Mathematical Problems in Engineering, 2014, 6 pp.
Sales-Teodoro, G., Tenreiro-Machado J.A., Capelas-de Oliveira, E. A review of definitions of fractional derivatives and other operators. Journal of Computational Physics, 388, 2019, 195-208.
Caputo, M., Fabrizio, M. A new definition of fractional derivative without singular kernel. Progress in Fractional Differentiation and Applications, 1 (2), 2015, pp. 1-13.
Atangana A., Baleanu D. New fractional derivatives with nonlocal and non-singular kernel: theory and application to heat transfer model. arXiv:1602.03408, 2016.
Shukla, A.K., Prajapati, J.C. On a generalization of Mittag-Leffler function and its properties. Journal of Mathematical Analysis and Applications, 336, 2007, 797-811.
Khalil, R., Al Horani, M., Yousef, A., Sababheh, M. A new definition of fractional derivative. Journal of Computational and Applied Mathematics, 264, 2014, 65-70.
Martínez, L., Rosales, J.J., Carreño, C.A., Lozano, J.M. Electrical circuits described by fractional conformable derivative. International Journal of Circuit Theory and Applications, 2018, 1-10.
Abdeljawad, T. On conformable fractional calculus. Journal of Computational and Applied Mathematics, 279, 2015, 57-66.
Chung, W.S. Fractional Newton mechanics with conformable fractional derivative. Journal of Computational and Applied Mathematics, 290, 2015, 150-158.
Xua, H., Jiang, X. Creep constitutive models for viscoelastic materials based on fractional derivatives. Computers and Mathematics with Applications, 73, 2017, 1377-1384.
Hristov, J. Response functions in linear viscoelastic constitutive equations and related fractional operators. Mathematical Modelling of Natural Phenomena, 14, 2019, 34 pp.
Gómez-Aguilar, J.F., Razo-Hernández, R., Granados-Lieberman, D. A physical interpretation of fractional calculus in observables terms: analysis of the fractional time constant and the transitory response. Revista Mexicana de Física, 60, 2014, 32-38.
Rosales-García, J., Andrade-Lucio, J.A., Shulika, O. Conformable derivative applied to experimental Newton’s law of cooling. Revista Mexicana de Física, 66 (2), 2020, 224-227.
Alvarez, F., Alegria, A., Colmenero, J. Relationship between the time-domain Kohlrausch-Williams-Watts and frequency-domain Havriliak-Negami relaxation functions. Physical Review B, 44, 7306, 1991.
Lukichev, A. Physical meaning of the stretched exponential Kohlrausch function. Physics Letters A, 383 (24), 2019, 2983-2987.
Das-Gupta, D.K. Polyethylene: Structure, morphology, molecular motion and dielectric property behavior. IEEE Electrical Insulation Magazine, 10 (3), 1994, 5-15.
Frank, A. Dielectric characterization. TA Instruments USA, APN032, 2012, 10 pp.
Ortega, A., Rosales, J.J. Newton’s law of cooling with fractional conformable derivative. Revista Mexicana de Física, 64, 2018, 172-175.
Mondol, A., Gupta, R., Das, S., Dutta, T. An insight into Newton’s cooling law using fractional calculus. Journal of Applied Physics, 123, 06490, 2018, 9 pp.
Ebaid, A., Masaedeh, B., El-Zahar, E. A New fractional model for the falling body problem. Chinese Physics Letters, 34 (2), 2017, 3 pp.
Abdelhakim, A.A., Tenreiro-Machado, J.A. A critical analysis of the conformable derivative. Nonlinear Dynamics, 95, 2019, 3063-3073.
Anderson, D.R., Camrud, E., Ulness, D.J. On the nature of the conformable derivative and its applications to physics. Journal of Fractional Calculus and Applications, 10 (2), 2019, 92-135.
