Abstract
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.
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