On the asymptotic stability of linear system of fractional-order difference equations

Raghib Abu-Saris; Qasem Al-Mdallal

doi:10.2478/s13540-013-0039-2

On the asymptotic stability of linear system of fractional-order difference equations

Raghib Abu-Saris
, Qasem Al-Mdallal

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

117 Citations (Scopus)

Abstract

In this paper we investigate the stability of the equilibrium solution of the νth order linear system of difference equations (Δ _a+ν-1^ν y)(t) = Λ y(t + ν - 1);t ∈ ℕ_a,a ∈ ℝ, and Λ ∈ ℝ ^{p × p}, subject to the initial condition y(a + ν - 1) = y - 1, where 0 < ν < 1 and y_-1 ∈ ℝ^p .

Original language	English
Pages (from-to)	613-629
Number of pages	17
Journal	Fractional Calculus and Applied Analysis
Volume	16
Issue number	3
DOIs	https://doi.org/10.2478/s13540-013-0039-2
Publication status	Published - Sept 2013

Keywords

Volterra difference equations
asymptotic stability
fractional-order difference equations
special functions

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.2478/s13540-013-0039-2

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abstract = "In this paper we investigate the stability of the equilibrium solution of the νth order linear system of difference equations (Δ a+ν-1ν y)(t) = Λ y(t + ν - 1);t ∈ ℕa,a ∈ ℝ, and Λ ∈ ℝ p × p, subject to the initial condition y(a + ν - 1) = y - 1, where 0 < ν < 1 and y-1 ∈ ℝp .",

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AU - Al-Mdallal, Qasem

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N2 - In this paper we investigate the stability of the equilibrium solution of the νth order linear system of difference equations (Δ a+ν-1ν y)(t) = Λ y(t + ν - 1);t ∈ ℕa,a ∈ ℝ, and Λ ∈ ℝ p × p, subject to the initial condition y(a + ν - 1) = y - 1, where 0 < ν < 1 and y-1 ∈ ℝp .

AB - In this paper we investigate the stability of the equilibrium solution of the νth order linear system of difference equations (Δ a+ν-1ν y)(t) = Λ y(t + ν - 1);t ∈ ℕa,a ∈ ℝ, and Λ ∈ ℝ p × p, subject to the initial condition y(a + ν - 1) = y - 1, where 0 < ν < 1 and y-1 ∈ ℝp .

KW - Volterra difference equations

KW - asymptotic stability

KW - fractional-order difference equations

KW - special functions

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JF - Fractional Calculus and Applied Analysis

IS - 3

ER -

On the asymptotic stability of linear system of fractional-order difference equations

Abstract

Keywords

ASJC Scopus subject areas

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