Geodesic
Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel
Morales-Delgado, V. F. 1 ; Gómez-Aguilar, J. F. 2 ; Taneco-Hernández, M. A.1 ; Escobar-Jiménez, R. F.3 ; Olivares-Peregrino, V. H. 3
1 Facultad de Matematicas, Universidad Autonoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria. Chilpancingo, Guerrero, Mexico
2 CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico
3 Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico
Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 8, p. 994-1014.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we analyze the fractional modeling of the giving up the smoking using the definitions of Liouville-Caputo and Atangana-Baleanu-Caputo fractional derivatives. Applying the homotopy analysis method and the Laplace transform with polynomial homotopy, the analytical solution of the smoking dynamics has obtained. Furthermore, using an iterative scheme by the Laplace transform, and the Atangana-Baleanu fractional integral, special solutions of the model are obtained. Uniqueness and existence of the solutions by the fixed-point theorem and Picard-Lindelof approach are studied. Finally, some numerical simulations are carried out for illustrating the results obtained.
DOI : 10.22436/jnsa.011.08.06
Classification : 92C50, 26A33, 44A10, 65H20
Keywords: Smoking model, Liouville-Caputo fractional derivative, Atangana-Baleanu fractional derivative, Laplace transform, homotopy method

Morales-Delgado, V. F.  1 ; Gómez-Aguilar, J. F.  2 ; Taneco-Hernández, M. A. 1 ; Escobar-Jiménez, R. F. 3 ; Olivares-Peregrino, V. H.  3

1 Facultad de Matematicas, Universidad Autonoma de Guerrero, Av. Lázaro Cárdenas S/N, Cd. Universitaria. Chilpancingo, Guerrero, Mexico
2 CONACyT-Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico
3 Tecnológico Nacional de México/CENIDET, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, Mexico 
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     author = {Morales-Delgado, V. F.  and G\'omez-Aguilar, J. F.  and Taneco-Hern\'andez, M. A. and Escobar-Jim\'enez, R. F. and Olivares-Peregrino, V. H. },
     title = {Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {994-1014},
     publisher = {mathdoc},
     volume = {11},
     number = {8},
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Morales-Delgado, V. F. ; Gómez-Aguilar, J. F. ; Taneco-Hernández, M. A.; Escobar-Jiménez, R. F.; Olivares-Peregrino, V. H. . Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel. Journal of nonlinear sciences and its applications, Tome 11 (2018) no. 8, p. 994-1014. doi : 10.22436/jnsa.011.08.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.011.08.06/

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