Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model

Algahtani, Obaid

doi:10.1016/j.chaos.2016.03.026

Cited by 194 publications

(92 citation statements)

References 10 publications

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“…In future analyses, it would be interesting to determine whether the methodology can be applied with equal success to other definitions of the fractional derivative that are commonly applied in circuit analyses, such as the Atangana-Baleanu definition [4,20] and others [3,5].…”

Section: Discussionmentioning

confidence: 99%

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Sowa

2018

Circuits Syst Signal Process

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This paper discusses the ability to obtain periodic steady-state solutions for fractional nonlinear circuit problems. For a class of nonlinear problems with fractional derivatives (based on the Caputo or Riemann-Liouville definitions), a methodology is proposed to derive equations representing the dependencies between the harmonics of the sought variables. Two approaches are considered for how to address the apparent nonlinear dependencies: one based on symbolic computation and the other a numerical approach based on the analysis of time functions. An example problem with fractional and nonlinear elements is presented to illustrate the usefulness of the proposed methodology. Two error criteria are introduced to verify the accuracy of the obtained results. The methodology is mainly designed to provide referential solutions in analyses of the numerical method called SubIval (the subinterval-based method for computation of the fractional derivative in initial value problems).

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Section: Discussionmentioning

confidence: 99%

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Sowa

2018

Circuits Syst Signal Process

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“…In this section, we present the definitions of the new fractional derivative with no singular and nonlocal kernel [1,3,4].…”

Section: Atangana-baleanu Derivatives In Caputo Sensementioning

confidence: 99%

Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators

Alkahtani¹,

Atangana²,

Koca³

2017

J. Nonlinear Sci. Appl.

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A mathematical system of equations using the concept of fractional differentiation with non-local and non-singular kernel has been analysed in this work. The developed mathematical model is designed to portray the spread of Zika virus within a given population. We presented the equilibrium point and also the reproductive number. The model was solving analytically using the Adams type predictor-corrector rule for Atangana-Baleanu fractional integral. The existence and uniqueness exact solution was presented under some conditions. The numerical replications were also presented.

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“…The Atangana-Baleanu fractional operator in Liouville-Caputo sense (ABC) is defined as follows [28][29][30][31][32][33] ABC a…”

Section: Fractional Derivativesmentioning

confidence: 99%

“…The resulting fractional operator is based on the exponential function [18][19][20][21][22][23][24][25][26][27]; however, the derivative proposed by Caputo and Fabrizio it is not a fractional derivative, its corresponding kernel is local. To solve the problem, Atangana and Baleanu suggested two news derivatives with Mittag-Leffler kernel, these operators in Liouville-Caputo and Riemann-Liouville have non-singular and non-local kernel and preserve the benefits of the Riemann-Liouville, Liouville-Caputo and Caputo-Fabrizio fractional operators [28][29][30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels

Gómez-Aguilar

Morales‐Delgado

Taneco-Hernández

et al. 2016

Entropy

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Abstract:In this work we obtain analytical solutions for the electrical RLC circuit model defined with Liouville-Caputo, Caputo-Fabrizio and the new fractional derivative based in the Mittag-Leffler function. Numerical simulations of alternative models are presented for evaluating the effectiveness of these representations. Different source terms are considered in the fractional differential equations. The classical behaviors are recovered when the fractional order α is equal to 1.

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Comparing the Atangana–Baleanu and Caputo–Fabrizio derivative with fractional order: Allen Cahn model

Cited by 194 publications

References 10 publications

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

A Harmonic Balance Methodology for Circuits with Fractional and Nonlinear Elements

Novel analysis of the fractional Zika model using the Adams type predictor-corrector rule for non-singular and non-local fractional operators

Analytical Solutions of the Electrical RLC Circuit via Liouville–Caputo Operators with Local and Non-Local Kernels

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