On Riemann and Caputo fractional differences

By using a linear feedback control technique, we propose a chaos synchronization scheme for nonlinear fractional discrete dynamical systems. Then, we construct a novel 1-D fractional discrete income change system and a kind of novel 3-D fractional discrete system. By means of the stability principles of Caputo-like fractional discrete systems, we lastly design a controller to achieve chaos synchronization, and present some numerical simulations to illustrate and validate the synchronization scheme.

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“…(Abdeljawad [36]). For 0 < ν, ν / ∈ N and x(t) defined on N a , the Caputo-like delta difference is defined by…”

Section: Definition 1 (Atici and Eloementioning

confidence: 99%

Chaos Synchronization of Nonlinear Fractional Discrete Dynamical Systems via Linear Control

Xin

Liu

Hou

et al. 2017

Entropy

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“…(Caputo Fractional Nabla Difference, [1]) The α th -order Caputo type Fractional Nabla Difference of u is given by…”

Section: Lemma 24 ([20]) For Any a B ∈ R The Quotient Expansion Omentioning

confidence: 99%

“…The unified definition for fractional nabla sum and differences is as follows. Definition 2.6 ( [1,15]). Let u : N a → R, α ∈ R and choose N ∈ N 1 such that N − 1 < α < N .…”

Section: Lemma 24 ([20]) For Any a B ∈ R The Quotient Expansion Omentioning

confidence: 99%

Solutions of fractional nabla difference equations - existence and uniqueness

Jonnalagadda

2016

OpMath

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“…The one step admissible set to (H, w) with respect to system (15) is defined by 1 (H, w) := {x ∈ R n : Hγ (X 0 , a + h, u(h)) ≤ w} The q step admissible set to (H, w) with respect to system (15) is defined by…”

Section: Definition 13mentioning

confidence: 99%

“…The first steps in this topic were made in [20]. Properties of the fractional sum, Caputo-and Riemman-Louville-type difference operators, were developed in [1][2][3][4]21]. Basic information on fractional calculus concept, ideas, and applications of these operators can be found for example in [15,18,24].…”

Section: Introductionmentioning

confidence: 99%

Remarks on Fractional Discrete Cone Control Systems with n-Orders and Their Stability

Girejko

Pawłuszewicz

2016

J Dyn Control Syst

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In the paper, fractional discrete cone control systems with n-orders are considered. Some relations between invariance and (asymptotic) stability properties of the presented systems are discussed. Operators employed to the considered systems are Caputo-, Riemman-Louville-, and Grünwald-Letnikov type ones. Cone systems with control, which are particular invariant systems with control, together with their stability and asymptotic stability properties are examined.

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On Riemann and Caputo fractional differences

Cited by 528 publications

References 12 publications

Chaos Synchronization of Nonlinear Fractional Discrete Dynamical Systems via Linear Control

Chaos Synchronization of Nonlinear Fractional Discrete Dynamical Systems via Linear Control

Solutions of fractional nabla difference equations - existence and uniqueness

Remarks on Fractional Discrete Cone Control Systems with n-Orders and Their Stability

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