2018
DOI: 10.1063/1.5054630
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Singular points in the solution trajectories of fractional order dynamical systems

Abstract: Dynamical systems involving non-local derivative operators are of great importance in Mathematical analysis and applications. This article deals with the dynamics of fractional order systems involving Caputo derivatives. We take a review of the solutions of linear dynamical systems C 0 D α t X(t) = AX(t), where the coefficient matrix A is in canonical form. We describe exact solutions for all the cases of canonical forms and sketch phase portraits of planar systems.We discuss the behavior of the trajectories w… Show more

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Cited by 21 publications
(13 citation statements)
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“…􏼉 is called the instability measure for equilibrium points in fractional-order systems (IMFOS). is measure is a necessary [47] but not a sufficient condition for the presence of chaos in a fractionalorder system [52][53][54].…”
Section: Definitions and Lemmamentioning
confidence: 98%
“…􏼉 is called the instability measure for equilibrium points in fractional-order systems (IMFOS). is measure is a necessary [47] but not a sufficient condition for the presence of chaos in a fractionalorder system [52][53][54].…”
Section: Definitions and Lemmamentioning
confidence: 98%
“…Remark 3. Recently Bhalekar et al [2] have numerically found that for a 2-dimensional linear fractional systems, self-intersection occurs in region |arg(λ ± )| = απ 2 + ǫ, for sufficiently small ǫ > 0 and λ ± being eigenvalues of system. This region comes as a direct consequence of Theorem 7 and the fact that zeros η α,k ∈ C of E α,0 (z) are located in |arg(z)| < απ 2 + ǫ, for large enough k ∈ N (See the proof of Theorem 4.7 in [9] ).…”
Section: Self Intersectionsmentioning
confidence: 99%
“…With the recent increase of studies and experiments with fractional order systems, the possibilities of finding new behaviors and better descriptions of natural phenomena are a recurring theme in the literature [22][23][24][25][26][27][28][29][30]. However, the use of this numerical tool has been neglected because it is used as a dynamical validation mechanism and the effects and physical implications associated with the use of fractional order derivatives are ignored.…”
Section: Introductionmentioning
confidence: 99%