Fractional conformable derivatives of Liouville–Caputo type with low-fractionality

Morales‐Delgado, V. F.; Gómez-Aguilar, J. F.; Escobar-Jiménez, R.F.; Taneco-Hernández, M.A.

doi:10.1016/j.physa.2018.03.018

Cited by 51 publications

(24 citation statements)

References 15 publications

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“…This fractional conformable derivative has been applied for modeling problems in different fields such as science, technology, and engineering with excellent results. ()…”

Section: Resultsmentioning

confidence: 99%

Determination of supercapacitor parameters based on fractional differential equations

Hidalgo‐Reyes

Gómez‐Aguilar

Escobar-Jiménez

et al. 2019

Circuit Theory & Apps

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In this paper, we estimate the parameter values of a fractional-order model of supercapacitors involving fractional derivatives of Liouville-Caputo, Caputo-Fabrizio, and Atangana-Baleanu and fractional conformable derivative in the Liouville-Caputo sense. We present the exact solution of the considered model using the properties of the Laplace transform operator together with the convolution theorem. They developed numerical simulations using each one of the fractional derivatives; the results were compared graphically with experimental data obtained from different supercapacitors using standard laboratory equipment. The nonlocal parameters involved in the equivalent electrical circuit for the supercapacitor model are recalculated for each fractional derivative using a particle swarm optimization algorithm for generating optimal solutions. KEYWORDS exponential decay-law, fractional calculus, fractional conformable derivative, Mittag-Leffler function, power-law, supercapacitor model Int J Circ Theor Appl. 2019;47:1225-1253.wileyonlinelibrary.com/journal/cta

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“…This fractional conformable derivative has been applied for modeling problems in different fields such as science, technology, and engineering with excellent results. ()…”

Section: Resultsmentioning

confidence: 99%

Determination of supercapacitor parameters based on fractional differential equations

Hidalgo‐Reyes

Gómez‐Aguilar

Escobar-Jiménez

et al. 2019

Circuit Theory & Apps

View full text Add to dashboard Cite

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“…Expansion of the conformable fractional derivative in the Liouville-Caputo sense of order = 2− , with ≤ 1. 44 Considering a = 0 in the conformable fractional derivative in the Liouville-Caputo sense given in Equation (5) and making the change of variable u = n (5) is given as follows:…”

Section: Basic Definitions and Fractional Conformable Decomposition Mmentioning

confidence: 99%

“…Expansion of the conformable fractional derivative in the Liouville-Caputo sense of order = 1− , with ≤ 1. 44 Considering n = 1 and = 1 − in Equation (8), we get…”

Section: Basic Definitions and Fractional Conformable Decomposition Mmentioning

confidence: 99%

“…41,42 Based on the concept of nonlocal derivative, in the work of Jarad et al, 43 the authors introduced new fractional integration and differentiation operators in the Riemann-Liouville, Hadamard, and Liouville-Caputo sense, these operators were computed by iterating conformable integrals. In the work of Morales-Delgado et al, 44 the authors proposed a novel fractional conformable derivative with low fractality, -expansion was developed for the cases when the order of fractional derivatives can be expressed as = 2 − and = 1 − , with ≤ 1.…”

Section: Introductionmentioning

confidence: 99%

“…The aim of the present paper is to apply the fractional conformable derivatives with low fractality proposed in the work of Morales-Delgado et al 44 to construct an iterative method based on the Adomian decomposition method, a found novel chaotic behaviors for the fractional conformable Chen's, Genesio-Tesi's, and Liu's attractors with low fractality. The application of these derivatives has not been previously presented in the literature to the study of chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fractional conformable attractors with low fractality

Morales‐Delgado

Gómez‐Aguilar

Escobar-Jiménez

2018

Math Methods in App Sciences

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In this paper, we considered a fractional conformable derivative of Liouville-Caputo type of fractional-order = n − , which contains a small perturbation and positive integer n values between [0;1] to obtain the solutions of three different fractional conformable attractors (Chen's attractor, Genesio-Tesi's attractor, and Liu's attractor). The fractional conformable Adomian decomposition method is applied to obtain an expansion of the fractional conformable derivative in = n − . The solutions of the fractional chaotic systems are calculated in the form of convergent series. We investigate the dynamics of these attractors by numerical simulations for different fractional orders values and parameter . KEYWORDSadomian decomposition method, chaos, fractional calculus, fractional conformable derivative, low-fractality 6378

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Dynamics and complexity analysis of the conformable fractional‐order two‐machine interconnected power system

2019

Math Methods in App Sciences

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In this paper, based on the Adomian decomposition method (ADM) semi analytical solution algorithm, dynamics and complexity of the conformable fractional‐order two‐machine interconnected power system are investigated numerically by the bifurcation diagram, Lyapunov exponents (LEs), chaos diagram, and modified multiscale sample entropy (MM‐SampEn) algorithm separately. The results show that the system has rich dynamics. The angular instability is found and its frequency of occurrence can be judged by the number of scrolls of the chaotic attractor. The coexisting attractors are observed by changing the initial value and the reason is discussed. The high‐complexity region is determined, and MM‐SampEn complexity can indicate different coexisting attractors of the system. The research results in this paper lay a theoretical basis for the application of the conformable fractional‐order two‐machine interconnected power system.

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Fractional conformable derivatives of Liouville–Caputo type with low-fractionality

Cited by 51 publications

References 15 publications

Determination of supercapacitor parameters based on fractional differential equations

Determination of supercapacitor parameters based on fractional differential equations

Fractional conformable attractors with low fractality

Dynamics and complexity analysis of the conformable fractional‐order two‐machine interconnected power system

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