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Fractional conformable attractors with low fractality
Author(s) -
MoralesDelgado V. F.,
GómezAguilar J. F.,
EscobarJiménez R. F.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5146
Subject(s) - conformable matrix , mathematics , attractor , adomian decomposition method , fractional calculus , perturbation (astronomy) , mathematical analysis , differential equation , physics , quantum mechanics
In this paper, we considered a fractional conformable derivative of Liouville‐Caputo type of fractional‐order α = n − ϵ , which contains a small perturbation ϵ 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 ϵ = n − α . 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 ϵ .