Fractional conformable attractors with low fractality

Abstract

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

Existence of mild solutions for impulsive neutral Hilfer fractional evolution equations

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

“…Recently, Khalil et al 5 proposed a new fractional derivative called the conformable fractional‐order derivative, which has attracted the attention of many scholars because of its many new features compared with the most commonly used Riemann‐Liouville definition and Caputo definition 6 . And some relevant studies have been carried out 7‐17. Atangana et al 7 has continued to develop the theory of the conformable fractional calculus and obtained some new theorems and properties, which laid a theoretical foundation for the further research.…”

“…6 And some relevant studies have been carried out. [7][8][9][10][11][12][13][14][15][16][17] Atangana et al 7 has continued to develop the theory of the conformable fractional calculus and obtained some new theorems and properties, which laid a theoretical foundation for the further research. Khalil et al 8 obtained the numerical solution of the conformable fractional thermal conduction equation by making full use of the properties of the conformable calculus.…”

“…The analyzing results show the effectiveness of the proposed methods and the potential application values of the conformable fractional-order chaotic systems. Furthermore, previous studies [15][16][17] investigated the fractional conformable nonlinear systems with fractional conformable derivatives in the Liouville-Caputo sense. Especially, the low fractality, chaotic attractors, and dynamical behaviors are analyzed.…”

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