On explicit stability conditions for a linear fractional difference system
The paper describes the stability area for the difference system (Δαy)(n + 1 − α) = Ay(n), n= 0, 1,..., with the Caputo forward difference operator Δα of a real order α ∈ (0, 1) and a real constant matrix A. Contrary to the existing result on this topic, our stability conditions are fully explicit a...
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| Published in | Fractional calculus & applied analysis Vol. 18; no. 3; pp. 651 - 672 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
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01.06.2015
De Gruyter Open Nature Publishing Group |
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| Abstract | The paper describes the stability area for the difference system (Δαy)(n + 1 − α) = Ay(n), n= 0, 1,..., with the Caputo forward difference operator Δα of a real order α ∈ (0, 1) and a real constant matrix A. Contrary to the existing result on this topic, our stability conditions are fully explicit and involve the decay rate of the solutions. Some comparisons with a difference system of the Riemann- Liouville type are discussed as well, including related consequences and illustrating examples. |
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| AbstractList | The paper describes the stability area for the difference system (Δ[α]y)(n + 1 - α) = Ay(n), n= 0, 1, . . . , with the Caputo forward difference operator Δ[α] of a real order α ∈ (0, 1) and a real constant matrix A. Contrary to the existing result on this topic, our stability conditions are fully explicit and involve the decay rate of the solutions. Some comparisons with a difference system of the Riemann- Liouville type are discussed as well, including related consequences and illustrating examples. The paper describes the stability area for the difference system (Δ y)(n + 1 − α) = Ay(n), n= 0, 1, . . . , with the Caputo forward difference operator Δ of a real order α ∈ (0, 1) and a real constant matrix A. Contrary to the existing result on this topic, our stability conditions are fully explicit and involve the decay rate of the solutions. Some comparisons with a difference system of the Riemann- Liouville type are discussed as well, including related consequences and illustrating examples. The paper describes the stability area for the difference system (Δαy)(n + 1 − α) = Ay(n), n= 0, 1,..., with the Caputo forward difference operator Δα of a real order α ∈ (0, 1) and a real constant matrix A. Contrary to the existing result on this topic, our stability conditions are fully explicit and involve the decay rate of the solutions. Some comparisons with a difference system of the Riemann- Liouville type are discussed as well, including related consequences and illustrating examples. |
| Author | Győri, István Nechvátal, Ludĕk Čermák, Jan |
| Author_xml | – sequence: 1 givenname: Jan surname: Čermák fullname: Čermák, Jan email: cermak.j@fme.vutbr.cz organization: Institute of Mathematics, Brno University of Technology – sequence: 2 givenname: István surname: Győri fullname: Győri, István organization: Department of Mathematics, University of Pannonia Pf 158 – sequence: 3 givenname: Ludĕk surname: Nechvátal fullname: Nechvátal, Ludĕk organization: Institute of Mathematics, Brno University of Technology Technická 2 |
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| Keywords | Caputo difference operator Riemann-Liouville difference operator Primary 26A33 Secondary 34A08, 39A12, 39A30 asymptotic stability fractional-order difference system |
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| Snippet | The paper describes the stability area for the difference system (Δαy)(n + 1 − α) = Ay(n), n= 0, 1,..., with the Caputo forward difference operator Δα of a... The paper describes the stability area for the difference system (Δ y)(n + 1 − α) = Ay(n), n= 0, 1, . . . , with the Caputo forward difference operator Δ of a... The paper describes the stability area for the difference system (Δ[α]y)(n + 1 - α) = Ay(n), n= 0, 1, . . . , with the Caputo forward difference operator Δ[α]... |
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| SubjectTerms | Abstract Harmonic Analysis Analysis asymptotic stability Caputo difference operator fractional-order difference system Functional Analysis Integral Transforms Mathematics Operational Calculus Research Paper Riemann-Liouville difference operator |
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| Title | On explicit stability conditions for a linear fractional difference system |
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