Modeling diffusive transport with a fractional derivative without singular kernel

Gómez-Aguilar, J. F.; López, G.; Alvarado-Martínez, V.M.; Reyes-Reyes, J.; Medina, Manuel Adam

doi:10.1016/j.physa.2015.12.066

Cited by 99 publications

(28 citation statements)

References 31 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We used the local derivative in one model, the Caputo derivative with power function kernel with singularity and the Caputo-Fabrizio derivative with exponential kernel, which has no singularity [21][22][23][24]. We presented the existence and uniqueness of the model with local derivative and then we derived approximate solutions via iterative method.…”

Section: Discussionmentioning

confidence: 99%

Chaos on the Vallis Model for El Niño with Fractional Operators

Alkahtani

Atangana

2016

Entropy

View full text Add to dashboard Cite

Abstract:The Vallis model for El Niño is an important model describing a very interesting physical problem. The aim of this paper is to investigate and compare the models using both integer and non-integer order derivatives. We first studied the model with the local derivative by presenting for the first time the exact solution for equilibrium points, and then we presented the exact solutions with the numerical simulations. We further examined the model within the scope of fractional order derivatives. The fractional derivatives used here are the Caputo derivative and Caputo-Fabrizio type. Within the scope of fractional derivatives, we presented the existence and unique solutions of the model. We derive special solutions of both models with Caputo and Caputo-Fabrizio derivatives. Some numerical simulations are presented to compare the models. We obtained more chaotic behavior from the model with Caputo-Fabrizio derivative than other one with local and Caputo derivative. When compare the three models, we realized that, the Caputo derivative plays a role of low band filter when the Caputo-Fabrizio presents more information that were not revealed in the model with local derivative.

show abstract

Section: Discussionmentioning

confidence: 99%

Chaos on the Vallis Model for El Niño with Fractional Operators

Alkahtani

Atangana

2016

Entropy

View full text Add to dashboard Cite

show abstract

“…The two-parametric, three-parametric, four-parametric and multiple Mittag-Leffler functions were presented by Wiman, Prabhakar, Shukla and Srivastava in [13][14][15][16][17][18]. The kernel used in Atangana-Baleanu fractional differentiation appears naturally in several physical problems as generalized exponential decay and as a power-law asymptotic for a very large time [19][20][21][22][23][24]. The choice of this derivative is motivated by the fact that the interaction is not local, but global, and also, the trend observed in the field does not follow the power-law.…”

Section: Introductionmentioning

confidence: 99%

Fractional Derivatives with the Power-Law and the Mittag–Leffler Kernel Applied to the Nonlinear Baggs–Freedman Model

Gómez-Aguilar

Atangana

2018

Fractal Fract

View full text Add to dashboard Cite

This paper considers the Freedman model using the Liouville-Caputo fractional-order derivative and the fractional-order derivative with Mittag-Leffler kernel in the Liouville-Caputo sense. Alternative solutions via Laplace transform, Sumudu-Picard and Adams-Moulton rules were obtained. We prove the uniqueness and existence of the solutions for the alternative model. Numerical simulations for the prediction and interaction between a unilingual and a bilingual population were obtained for different values of the fractional order.

show abstract

“…A model of resistance, inductance, capacitance circuit using the Caputo-Fabrizio operator with fractional order is proposed in [6]. In [11], the authors applied the CaputoFabrizio operator to the diffusion and the diffusion-advection equation. In [7], Baleanu et al studied the existence of solutions for some infinite coefficient-symmetric CaputoFabrizio fractional integro-differential equations.…”

Section: Introductionmentioning

confidence: 99%