TY - JOUR AU - Morales-Delgado, V. F. AU - Gómez-Aguilar, J. F. AU - Taneco-Hernández, M. A. AU - Escobar-Jiménez, R. F. AU - Olivares-Peregrino, V. H. PY - 2018 TI - Mathematical modeling of the smoking dynamics using fractional differential equations with local and nonlocal kernel JO - Journal of Nonlinear Sciences and Applications SP - 994--1014 VL - 11 IS - 8 AB - 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. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.011.08.06 DO - 10.22436/jnsa.011.08.06 ID - Morales-Delgado2018 ER - TY - JOUR TI - Mathematical study of smoking model by incorporating campaign class AU - O. J. Algahtani AU - A. Zeb AU - G. Zaman AU - S. Momani AU - I. H. Jung JO - Wulfenia PY - 2015 DA - 2015// VL - 22 ID - Algahtani2015 ER - TY - JOUR TI - Chua’s circuit model with Atangana-Baleanu derivative with fractional order AU - B. S. T. Alkahtani JO - Chaos Solitons Fractals PY - 2016 DA - 2016// VL - 89 ID - Alkahtani 2016 ER - TY - JOUR TI - New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model AU - A. Atangana AU - D. Baleanu JO - Therm Sci. 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